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मान ज्ञात कीजिए int (0)^(pi) (x sin x)/(...

मान ज्ञात कीजिए `int _(0)^(pi) (x sin x)/(1+cos^(2)x)dx`

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

int_(0)^(pi) x sin x cos^(2)x\ dx

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

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

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

int_(0)^(pi)(cos x)/(1-sin^(m)x)dx

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

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

int_(0)^( pi)x*sin x*cos^(4)x*dx

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