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" *19."int(-pi)^( pi)(2x(1+sin x))/(1+co...

" *19."int_(-pi)^( pi)(2x(1+sin x))/(1+cos^(2)x)dx

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Evaluate: int_(-pi)^( pi)((2x)(1+sin x)/(1+cos^(2)x))dx

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

int_(-pi)^(pi) (2x(1 + sin x))/(1 + cos^2 x) dx is :

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

int_(-pi)^(pi)(1-x^(2))sin x cos^(2)x dx=

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

int_((pi)/(2))^(pi)(1-sin x)/(1-cos x)dx

int_(-pi)^(pi) (x Cos x)/(1+Sin^(2)x)dx=

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