What is the integral of cot^6(x)csc^2(x) ?

The integral of cot^6(x)csc^2(x) is -(cot^7(x))/7+C

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integral of cot^6(x)csc^2(x)

\int cot^{6} (x) csc^{2} (x) d x

- \frac{cot ^{7} ( x )}{7} + C

Solution steps

\int cot^{6} (x) csc^{2} (x) d x

Apply u-substitution

= \int - u^{6} d u

Take the constant out:

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

= - \int u^{6} d u

Apply the Power Rule

= - \frac{u ^{7}}{7}

Substitute back

u = cot (x)

= - \frac{cot ^{7} ( x )}{7}

Add a constant to the solution

= - \frac{cot ^{7} ( x )}{7} + C

What is the integral of cot^6(x)csc^2(x) ?
The integral of cot^6(x)csc^2(x) is -(cot^7(x))/7+C