Home
Class 12
MATHS
Evaluate: int1/(sinx(2cos^(2)x-1))dx...

Evaluate: `int1/(sinx(2cos^(2)x-1))dx`

Text Solution

Verified by Experts

Putting `cosx=t`, we get
`I=int(1/(sinx(2cos^(2)x-1)))dx=int(1/(sinx(2t^(2)-1))xx -(dt)/(sinx))=-int1/((1-t^(2)(2t^(2)-1))`dt
`therefore I=-int(1/(1-t^(2))+2/(2t^(2)-1))dt=-int1/(1-t^(2))dt-2int1/(2t^(2)-1)dt`
`=-1/2ln |(1+t)/(1-t)|-sqrt(2)/2ln |(sqrt(2)t-1)/(sqrt(2)t+1)|+C=-1/2ln|(1+cosx)/(1-cosx)|-1/sqrt(2)ln|(sqrt(2)cosx-1)/(sqrt(2)cosx+1)|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise EXERCISE -1 SUBJECTIVE QUESTIONS|1 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SUBJECTIVE QUESTIONS|14 Videos

  • GEOMETRY

    RESONANCE|Exercise Exercise-1 (Part-I: Previous Asked Question For Pre RMO)|50 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

Similar Questions

Explore conceptually related problems

Evaluate : int(1)/(sinx.cos^(2)x)dx

Evaluate int(dx)/(sinx(3+cos^(2)x))

int(sinx)/((1+cos^(2)x))dx

Evaluate: int 1/(sinx cos^3x) dx

Evaluate: int1/(3+2sinx+cosx)dx

Evaluate : int(sinx)/(cos^(9//2)x)dx

int(1)/(sinx*cos^(2)x)dx=

Evaluate: int1/(cosx(sinx+2cosx))\ dx

int(1)/(sinx.cos^(3)x)dx=

Evaluate: int1/((2sinx+3cosx)^2)\ dx