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int(0)^(pi//4)(tan^(3)x)/((1+cos2x))dx...

`int_(0)^(pi//4)(tan^(3)x)/((1+cos2x))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(8)`
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Evaluate the following integral: int_0^(pi//4)(tan^3x)/(1+cos2x)dx

int_(0)^(pi//4) tan x dx

int_(0)^(pi//4)(dx)/((1+cos2x))

int_(0)^(pi//4)(1-tan x)/(1+tan x)dx =

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

int_(pi//4)^(pi//2)(dx)/((1-cos2x))

int_(0)^(pi//2)(1)/(1+tan^(3)x)dx=

The value of I=int_(0)^(pi//4)(tan^(*n+1)x)dx+(1)/(2)int_(0)^(pi//2)tan^(n-1)((x)/(2))dx is equal to

int_(0)^(pi//4) (1)/(1+cos 2x)dx

int_(pi//4)^(3pi//4)(dx)/(1+cos x)=