What is the integral of cot^3(y)csc^2(y) ?

The integral of cot^3(y)csc^2(y) is -(cot^4(y))/4+C

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integral of cot^3(y)csc^2(y)

\int cot^{3} (y) csc^{2} (y) d y

- \frac{cot ^{4} ( y )}{4} + C

Solution steps

\int cot^{3} (y) csc^{2} (y) d y

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cot (y)

= - \frac{cot ^{4} ( y )}{4}

Add a constant to the solution

= - \frac{cot ^{4} ( y )}{4} + C

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What is the integral of cot^3(y)csc^2(y) ?
The integral of cot^3(y)csc^2(y) is -(cot^4(y))/4+C