What is the integral of cot^7(x)csc^2(x) ?

The integral of cot^7(x)csc^2(x) is -(cot^8(x))/8+C

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integral of cot^7(x)csc^2(x)

\int cot^{7} (x) csc^{2} (x) d x

- \frac{cot ^{8} ( x )}{8} + C

Solution steps

\int cot^{7} (x) csc^{2} (x) d x

Apply Trigonometric Substitution

: \int - u^{7} d u

= \int - u^{7} d u

Take the constant out:

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

= - \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= - \frac{u ^{8}}{8}

Substitute back

u = cot (x)

= - \frac{cot ^{8} ( x )}{8}

Add a constant to the solution

= - \frac{cot ^{8} ( x )}{8} + C

y = - 10

\frac{d}{d y} (x^{2 y})

36 y^{^{''}} + 36 y^{^{'}} + 11 y = 0, y (0) = 6, y^{^{'}} (0) = 5

\frac{6}{3 x + 1}, at a = - 1

What is the integral of cot^7(x)csc^2(x) ?
The integral of cot^7(x)csc^2(x) is -(cot^8(x))/8+C