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Derivative of Some Standard Functions

Integral 1+co...

Question

Integral 1+cos^2x/1-cos2x.dx

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Solution

+cos(2x)=2cos2(x)

1-cos(2x)=2sin2(x)

Integral of 1+COS2x/ 1-COS2x=Integral of 2cos2x/2sin2x = Integral of cot2x = Integral of {1- cosec2x}

= Integral od 1 dx - Integral of cosec2x dx = x - (- cotx )+ C = x + cotx +c
ans = x+cotx+c

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