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

= \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}

= - \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

\int \frac{1}{x ^{0.5}} d x

\frac{d}{d x} (\frac{2 x - x ^{2}}{3 x ^{2} + 1})

(- 5) (0.1)

x y^{2} y^{^{'}} = y^{3} - x^{3}, y (1) = 3

x \to 32 lim (\frac{x ^{2}}{4} - \frac{8}{x})

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