What is the integral of cot^4(x)csc^2(x) ?

The integral of cot^4(x)csc^2(x) is -(cot^5(x))/5+C

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integral of cot^4(x)csc^2(x)

\int cot^{4} (x) csc^{2} (x) d x

- \frac{cot ^{5} ( x )}{5} + C

Solution steps

\int cot^{4} (x) csc^{2} (x) d x

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

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

= - \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - \frac{u ^{5}}{5}

Substitute back

u = cot (x)

= - \frac{cot ^{5} ( x )}{5}

Add a constant to the solution

= - \frac{cot ^{5} ( x )}{5} + C

\int - sin (x) + \frac{1}{cos ^{2} ( x )} d x

\int x^{2} - ln (x^{2}) + k d x

\int_{1}^{5} 1 d x

\int x^{2} \cdot e^{- a x} d x

\frac{1}{( x - 1 )}

What is the integral of cot^4(x)csc^2(x) ?
The integral of cot^4(x)csc^2(x) is -(cot^5(x))/5+C