∫xx+2 dx - Mathematics and Statistics

Advertisements
Advertisements
Sum

`int x/(x + 2)  "d"x`

Advertisements

Solution

`int x/(x + 2)  "d"x = int ((x + 2) - 2)/(x + 2) "d"x`

= `int(1 - 2/(x + 2)) "d"x`

= `int 1 *"d"x - 2 int 1/(x + 2)  "d"x`

= x − 2log |x + 2| + c

  Is there an error in this question or solution?
Chapter 2.3: Indefinite Integration - Very Short Answers

RELATED QUESTIONS

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`


Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


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`


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

`1/(x-sqrtx)`


Integrate the functions:

`e^(2x+3)`


Integrate the functions:

`x/(e^(x^2))`


Integrate the functions:

tan2(2x – 3)


Integrate the functions:

sec2(7 – 4x)


Integrate the functions:

`1/(cos^2 x(1-tan x)^2`


Integrate the functions:

`1/(1 - tan x)`


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


Integrate the functions:

`(1+ log x)^2/x`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


Evaluate `int 1/(3+ 2 sinx + cosx) 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`


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

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

\[\int\cos x \sqrt{4 - \sin^2 x}\text{ dx}\]

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

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

\[\int\sqrt{16 x^2 + 25} \text{ dx}\]

\[\int\sqrt{4 x^2 - 5}\text{ dx}\]

Write a value of

\[\int \tan^3 x \sec^2 x \text{ dx }\].

 


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

 


Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


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\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]


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

 


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


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

 


Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]


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


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


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

 

 


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

\[\int x \sin^3 x\ dx\]

`int "dx"/(9"x"^2 + 1)= ______. `


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


Find : ` int  (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`


Integrate the following w.r.t. x : `3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`


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


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


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


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


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


Evaluate the following integrals:

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


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


Integrate the following functions w.r.t. x : `(logx)^n/x`


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


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


Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 


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


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

`(2sinx cosx)/(3cos^2x + 4sin^2 x)`


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


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


Integrate the following functions w.r.t. x : `x^5sqrt(a^2 + x^2)`


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


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


Integrate the following functions w.r.t. x : `sin(x - a)/cos(x  + b)`


Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`


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


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


Integrate the following functions w.r.t. x : cos7x


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


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


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


Evaluate the following : `int (1)/sqrt(2x^2 - 5).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)/(1 + x - x^2).dx`


Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`


Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`


Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`


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


Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`


Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`


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


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


Evaluate the following integrals:

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


Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`


Choose the correct options from the given alternatives :

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


`int logx/(log ex)^2*dx` = ______.


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*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)^2sqrt(x)`


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


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


Fill in the Blank.

`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______


Evaluate `int 1/((2"x" + 3))` dx


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


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int log ("x"^2 + "x")` dx


`int 2/(sqrtx - sqrt(x + 3))` dx = ________________


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


`int (log x)/(log ex)^2` dx = _________


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


`int sqrt(1 + sin2x)  "d"x`


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int logx/x  "d"x`


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


`int cot^2x  "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"`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`


Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`


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


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


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.


`int[ tan (log x) + sec^2 (log x)] dx= ` ______


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


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 (x + sinx)/(1 + cosx)dx` is equal to ______.


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


If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.


`int (logx)^2/x dx` = ______.


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


Evaluate the following.

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


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


Evaluate the following.

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


Solve the following Evaluate.

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


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


Evaluate the following

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


Evaluate:

`int sqrt((a - x)/x) dx`


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


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


Evaluate:

`int sin^3x cos^3x  dx`


Evaluate the following:

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


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


Evaluate the following.

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


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


Share
Notifications



      Forgot password?
Use app×