Home
Class 12
MATHS
Evaluate int (log(e)(1+sin^(2)x))/(cos^(...

Evaluate `int (log_(e)(1+sin^(2)x))/(cos^(2)x) dx`

Text Solution

Verified by Experts

The correct Answer is:
`log_(e)(1+sin^(2)x).tanx-2x+sqrt2tan^(-1)(sqrt2tanx)+C`
`int(log_(e)(1+sin^(2)x)dx)/(cos^(2)x)`
`=log_(e)(1+sin^(2)x).tanx-2int(sin^(2)x+1-1)/(1+sin^(2)x)`
`=log_(e)(1+sin^(2)x).tanx-2x+2 int(sec^(2)xdx)/(1+2tan^(2)x)`
`=log_(e)(1+sin^(2)x).tanx-2x+sqrt2tan^(-1)(sqrt2tanx)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Multiple Correct Answer Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Single Correct Answer Type|48 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx.

Evaluate int_(0)^(1) x e^(-2x) dx

Evaluate : int_(0)^(pi/2)(sin^(2)x + cos^(4)x)dx

Evaluate int_(0)^(pi/2)(sin^(2)x+cos^(4)x) dx

Evaluate int (cos 2x + 2 sin ^(2) x dx )/( cos^(2) x )

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

Evaluate int x^(2) log x dx

Evaluate int(x+1)/(x(x+log_(e)x))dx

Evaluate int((log x-1)/(1+(logx)^(2)))^(2)dx

Evaluate : int (1 - sin 2x) dx .