The value of ∫sinxsinx-cosxdx equals ______. - Mathematics (JEE Main)

Advertisements
Advertisements
MCQ
Fill in the Blanks

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

Options

  • `1/2x + 1/2log(sinx - cosx) + C`

  • `1/2x - 1/2log(sinx - cosx) + C`

  • x + log(sinx + cosx) + C

  • x – log(sinx + cosx) + C

Advertisements

Solution

The value of `intsinx/(sinx - cosx)dx` equals `underlinebb(1/2x + 1/2log(sinx - cosx) + C)`.

Explanation:

I = `1/2int(2sinx)/(sinx - cosx)dx`

= `1/2int((sinx - cosx) + (sinx + cosx))/(sinx - cosx)dx`

= `1/2int[1 + (sinx + cosx)/(sinx - cosx)]dx`

= `1/2x + 1/2log(sinx - cosx) + C`

  Is there an error in this question or solution?

RELATED QUESTIONS

Evaluate : `int (sinx)/sqrt(36-cos^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 `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`


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:

sin x ⋅ sin (cos x)


Integrate the functions:

sin (ax + b) cos (ax + b)


Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


Integrate the functions:

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


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


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


Solve: dy/dx = cos(x + y)


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`


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

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

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

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

Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


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


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\[\int a^x e^x \text{ dx }\]


Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 


Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]


Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].


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

 


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


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

 

 


The value of \[\int\frac{1}{x + x \log x} dx\] is


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


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

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


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


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


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 (cos2x)/sin^2x dx` 


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


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


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


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


Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`


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


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


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


Integrate the following functions w.r.t. x : sin4x.cos3x


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


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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


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


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


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 :  tan 3x tan 2x tan x


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


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


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


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


Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`


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


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


Evaluate the following integrals:

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


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


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


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives : 

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


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`


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


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


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


Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx


Evaluate the following.

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


If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______


Fill in the Blank.

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


Fill in the Blank.

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


Evaluate: `int "x" * "e"^"2x"` dx


`int 1/sqrt((x - 3)(x - 2))` dx = ________________


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


`int sqrt(x^2 + 2x + 5)` dx = ______________


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


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int logx/x  "d"x`


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


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


`int 1/(xsin^2(logx))  "d"x`


`int (cos2x)/(sin^2x)  "d"x`


`int cos^7 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 "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 ______ 


`int1/(4 + 3cos^2x)dx` = ______ 


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


`int (cos x)/(1 - sin x) "dx" =` ______.


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


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


The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.


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 ______.


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 ______.


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


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


Write `int cotx  dx`.


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


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


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


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


Evaluate the following.

`int x sqrt(1 + x^2)  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`


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 the following.

`int1/(x^2+4x-5) dx`


Evaluate:

`int(cos 2x)/sinx dx`


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


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


Evaluate the following

`int x^3 e^(x^2) ` dx


Evaluate the following.

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


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


Share
Notifications



      Forgot password?
Use app×