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int(0)^( pi/4)(sec x)/(1+2sin^(2)x)dx...

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

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int_(0)^(pi/4) (sec x)/(1+2 sin^(2)x) is equal to

" 0."int_(0)^( pi/4)(dx)/(2+sin^(2)x)=

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

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

int _(0)^((pi)/(4))(sec x dx)/(1+2 sin^(2)x)

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

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

int_(0)^( pi)(x)/(1+sin^(2)x)*dx