Integrate the following w.r.t. x : 2x3-5x+3x+4x5 - Mathematics and Statistics

Advertisements
Advertisements
Sum

Integrate the following w.r.t. x : `2x^3 - 5x + 3/x + 4/x^5`

Advertisements

Solution

`int(2x^3 - 5x + 3/x + 4/x^5)dx`

= `2intx^3 dx - 5 int x dx + 3 int1/x dx + 4 int x^-5 dx`

= `2(x^4/4) - 5(x^2/2) + 3 log |x| + 4(x/(-4)) + c`

= `x^4/(2) - (5)/(2) x^2 + 3 log |x| - (1)/x^4 + c`

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.1 [Page 102]

APPEARS IN

RELATED QUESTIONS

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`


Evaluate :`intxlogxdx`


Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Evaluate :

`int(sqrt(cotx)+sqrt(tanx))dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Find : `int(x+3)sqrt(3-4x-x^2dx)`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

`xsqrt(x + 2)`


Integrate the functions:

`(x^3 - 1)^(1/3) x^5`


Integrate the functions:

`x^2/(2+ 3x^3)^3`


Integrate the functions:

tan2(2x – 3)


Integrate the functions:

`(sin^(-1) x)/(sqrt(1-x^2))`


Integrate the functions `cos x /(sqrt(1+sinx))`


Integrate the functions cot x log sin x


Integrate the functions in `1/(1 + cot x)`


Integrate the functions in `sqrt(tanx)/(sinxcos x)`


Choose the correct answer `int (dx)/(sin^2 x cos^2 x)` equals

(A) tan x + cot x + C

(B) tan x – cot x + C

(C) tan x cot x + C

(D) tan x – cot 2x + C


Evaluate : `∫1/(3+2sinx+cosx)dx`


Evaluate: `int 1/(x(x-1)) dx`


Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`


Evaluate: `int (2y^2)/(y^2 + 4)dx`


Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`


Evaluate: `int (sec x)/(1 + cosec x) dx`


\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]

\[\int\sqrt{9 - x^2}\text{ dx}\]

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

 Write a valoue of \[\int \sin^3 x \cos x\ dx\]

 


Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]


Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]


Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


Write a value of\[\int \log_e x\ dx\].

 


Write a value of

\[\int e^{2 x^2 + \ln x} \text{ dx}\]

Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]


Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


Write a value of\[\int e^{ax} \sin\ bx\ dx\]


Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .


Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .


Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]


Evaluate:  \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]


\[\text{ If } \int\left( \frac{x - 1}{x^2} \right) e^x dx = f\left( x \right) e^x + C, \text{ then  write  the value of  f}\left( x \right) .\]

\[\int\frac{\cos^5 x}{\sin x} \text{ dx }\]

Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`


 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`


 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`


Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`


Evaluate the following integrals : tan2x dx


Evaluate the following integrals : `int (sin2x)/(cosx)dx`


Evaluate the following integrals : `int sin x/cos^2x dx`


Evaluate the following integrals : `int tanx/(sec x + tan x)dx`


Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`


Evaluate the following integrals : `int sin 4x cos 3x dx`


Evaluate the following integrals:

`int x/(x + 2).dx`


Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`


Evaluate the following integrals : `int cos^2x.dx`


Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`


If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)


Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`


Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`


Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`


Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`


Integrate the following functions w.r.t.x:

cos8xcotx


Integrate the following functions w.r.t. x : tan5x


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Integrate the following functions w.r.t. x : sin5x.cos8x


Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`


Evaluate the following : `int (1)/(4x^2 - 3).dx`


Evaluate the following : `int (1)/(7 + 2x^2).dx`


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`


Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`


Evaluate the following integrals :  `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`


Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`


Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`


Evaluate the following : `int (logx)2.dx`


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =


Choose the correct options from the given alternatives :

`int (e^(2x) + e^-2x)/e^x*dx` =


integrate the following with respect to the respective variable : `x^2/(x + 1)`


If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).


Evaluate the following.

`int "x"^3/sqrt(1 + "x"^4)` dx


Evaluate the following.

`int "x"^5/("x"^2 + 1)`dx


Evaluate the following.

`int 1/("x"("x"^6 + 1))` dx


Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx


Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx


Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


Fill in the Blank.

To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________


Evaluate `int "x - 1"/sqrt("x + 4")` dx


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int 1/(sqrt("x") + "x")` dx


`int 1/(cos x - sin x)` dx = _______________


`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________


If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______


`int logx/x  "d"x`


`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


Evaluate `int(3x^2 - 5)^2  "d"x`


`int (1 + x)/(x + "e"^(-x))  "d"x`


`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?


`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?


If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 


If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.


`int(sin2x)/(5sin^2x+3cos^2x)  dx=` ______.


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.


If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.


If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.


`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).


`int(log(logx) + 1/(logx)^2)dx` = ______.


`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.


The value of `intsinx/(sinx - cosx)dx` equals ______.


If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


`int 1/(sinx.cos^2x)dx` = ______.


The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.


`int cos^3x  dx` = ______.


`int secx/(secx - tanx)dx` equals ______.


Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`


if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`


If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)


Evaluate.

`int(5"x"^2 - 6"x" + 3)/(2"x" - 3)  "dx"`


Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`


Evaluate the following.

`int x^3/(sqrt(1 + x^4))dx`


Evaluate the following.

`int 1/(x^2 + 4x - 5)dx`


Prove that:

`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`


If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)


Evaluate the following.

`int(1)/(x^2 + 4x - 5)dx`


Evaluate:

`int sin^2(x/2)dx`


Evaluate `int 1/(x(x-1))dx`


Evaluate.

`int (5x^2-6x+3)/(2x-3)dx`


`int x^2/sqrt(1 - x^6)dx` = ______.


`int 1/(sin^2x cos^2x)dx` = ______.


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


Evaluate the following:

`int x^3/(sqrt(1+x^4))dx`


Evaluate `int(1+x+x^2/(2!))dx`


Evaluate `int (1 + "x" + "x"^2/(2!))`dx


Evaluate.

`int (5x^2 -6x + 3)/(2x -3)dx`


Evaluate `int1/(x(x-1))dx`


If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Share
Notifications



      Forgot password?
Use app×