Definite Integral 1

∫0pi/42tanxsinx1+sin2xdx

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1
sidharthkumar ·

write
I= 2sin^2 x / cosx(1+sin^2x)
I/2 = 1+sin^2 x -1 / cosx(1+sin^2x)
I/2= int (0 to pi/4) secx dx -2 int (0 to pi/4) cos x dx / 1-sin^4x
solve it to get
I= 2log(sqrt(2) - 1 ) - (1/2)*log(sqrt(2)-1 / sqrt(2) +1 + tan(inv.) 1/sqrt(2)

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