Home
Class 12
MATHS
If int(3cot3x-cotx)/(tanx-3tan3x)dx = pf...

If `int(3cot3x-cotx)/(tanx-3tan3x)dx = pf(x) + qg(x)+C`, then which of the following may be correct?

A

`p=1,q=1/sqrt(3), f(x)=x,g(x)="ln"|(sqrt(3)-tanx)/(sqrt(3)+tanx)|`

B

`p=1, q=-1/sqrt(3), f(x)=x,g(x)="ln"|(sqrt(3)-tanx)/(sqrt(3)+tanx)|`

C

`p=1, q=-2/sqrt(3), f(x)=x,g(x)="ln"|(sqrt(3)+tanx)/(sqrt(3)-tanx)|`

D

`p=1, q=-1/sqrt(3),f(x)=x,g(x)="ln"|(sqrt(3)+tanx)/(sqrt(3)-tanx)|`

Text Solution

AI Generated Solution

To solve the integral \[ I = \int \frac{3 \cot(3x) - \cot(x)}{\tan(x) - 3 \tan(3x)} \, dx \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise COMPREHENSION|5 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise Exercise-3 Part I- JEE ADVANCED/ IIT-JEE PROBLEMS|8 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SINGLE AND DOUBLE VALUE INTEGER TYPE|16 Videos

  • FUNDAMENTAL OF MATHEMATICS

    RESONANCE ENGLISH|Exercise Exercise|135 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos

Similar Questions

Explore conceptually related problems

int(1+cos4x)/(cotx-tanx)dx

int(cotx+cot^3x)/(1+cot^3x)dx

int tanx.tan2x.tan3xdx =

int(cos4x-1)/(cotx-tanx)dx is equal to

int(1+cos4x)/(cotx-tanx)\ dx

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?

If cos2x-3cosx+1=(cos e c\ x)/(cotx-cot2x),\ then which of the following is true ?

int( x^3)/(x^2-3)dx

int cot^3 x dx

int(cos 4x-1)/(cot x-tanx)dx is equal to