What is the integral of sin^2(x)cot(x) ?

The integral of sin^2(x)cot(x) is (sin^2(x))/2+C

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integral of sin^2(x)cot(x)

\int sin^{2} (x) cot (x) d x

\frac{sin ^{2} ( x )}{2} + C

Solution steps

\int sin^{2} (x) cot (x) d x

Express with sin, cos

= \int cos (x) sin (x) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= \frac{sin ^{2} ( x )}{2}

Add a constant to the solution

= \frac{sin ^{2} ( x )}{2} + C

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What is the integral of sin^2(x)cot(x) ?
The integral of sin^2(x)cot(x) is (sin^2(x))/2+C