What is the integral of (cos(x))/(sin^{12)(x)} ?

The integral of (cos(x))/(sin^{12)(x)} is -1/11 csc^{11}(x)+C

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integral of (cos(x))/(sin^{12)(x)}

\int \frac{cos ( x )}{sin ^{12} ( x )} d x

- \frac{1}{11} csc^{11} (x) + C

Solution steps

\int \frac{cos ( x )}{sin ^{12} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{12}} d u

= \int \frac{1}{u ^{12}} d u

Apply the Power Rule

: - \frac{1}{11 u ^{11}}

= - \frac{1}{11 u ^{11}}

Substitute back

u = sin (x)

= - \frac{1}{11 sin ^{11} ( x )}

Simplify

- \frac{1}{11 sin ^{11} ( x )} : - \frac{1}{11} csc^{11} (x)

= - \frac{1}{11} csc^{11} (x)

Add a constant to the solution

= - \frac{1}{11} csc^{11} (x) + C

y = e

f (x) = \frac{4}{x - 1}

96 s^{2} + 117 s + 108

\int 4^{2 - 3 x} d x

\frac{48}{s ( s + 4 ) ^{2} ( s + 3 )}

What is the integral of (cos(x))/(sin^{12)(x)} ?
The integral of (cos(x))/(sin^{12)(x)} is -1/11 csc^{11}(x)+C