Question

Integrate stang-coto)" dx​

Answer 1

Strategy: Make in terms of sin's and cos's; Use Subtitution.

(integral) cot x dx = (integral) cos x

sin x dx

set

u = sin x.

then we find

du = cos x dx

substitute du=cos x, u=sin x

(integral) cos x

sin x dx = (integral)

du

u

solve integral

= ln |u| + C

substitute back u=sin x

= ln |sin x| + C

Q.E.D.

Answer 2

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