Integration(0 to pi/2) x/sinx+cosx
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in the numerator that should be sin x.
denominator is sin x + cos x
rewrite that numerator as : 1/2 * [ sin x + cos x + sin x - cos x]
integrand is 1/2 - 1/2 * [ cos x - sin x]/[sin x + cos x]
integral is = x/2 - 1/2 * Log | sin x + cos x |
value after substituting the limits :
π/4
denominator is sin x + cos x
rewrite that numerator as : 1/2 * [ sin x + cos x + sin x - cos x]
integrand is 1/2 - 1/2 * [ cos x - sin x]/[sin x + cos x]
integral is = x/2 - 1/2 * Log | sin x + cos x |
value after substituting the limits :
π/4
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