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

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

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

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

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

Solution steps

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

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 (x)

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

Add a constant to the solution

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

2 x^{2} cos (x) cot (x)

f (x) = 5

\frac{d}{d x} (cos (9 sin (x)))

\frac{d}{d x} ((tan^{2} (x) - x^{2})^{3})

\int_{0}^{1} \frac{1 + x}{1 + 2 x} d x

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