What is the integral of (cos(x))/(sin^{16)(x)} ?

The integral of (cos(x))/(sin^{16)(x)} is -1/15 csc^{15}(x)+C

Popular >

integral of (cos(x))/(sin^{16)(x)}

\int \frac{cos ( x )}{sin ^{16} ( x )} d x

- \frac{1}{15} csc^{15} (x) + C

Solution steps

\int \frac{cos ( x )}{sin ^{16} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{16}} d u

= \int \frac{1}{u ^{16}} d u

Apply the Power Rule

: - \frac{1}{15 u ^{15}}

= - \frac{1}{15 u ^{15}}

Substitute back

u = sin (x)

= - \frac{1}{15 sin ^{15} ( x )}

Simplify

- \frac{1}{15 sin ^{15} ( x )} : - \frac{1}{15} csc^{15} (x)

= - \frac{1}{15} csc^{15} (x)

Add a constant to the solution

= - \frac{1}{15} csc^{15} (x) + C

\frac{x}{x + 7}

n = 0 \sum \infty \frac{1}{( 2 n + 1 )}

\frac{d}{d x} (1 - e^{c o s (1 - x^{2})})

y = arcsin (x^{2})

\int_{1}^{\infty} x^{- 9} d x

What is the integral of (cos(x))/(sin^{16)(x)} ?
The integral of (cos(x))/(sin^{16)(x)} is -1/15 csc^{15}(x)+C