What is the integral of (cos(x))/(sin^{10)(x)} ?

The integral of (cos(x))/(sin^{10)(x)} is -1/9 csc^9(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(x))/(sin^{10)(x)}

\int \frac{cos ( x )}{sin ^{10} ( x )} d x

- \frac{1}{9} csc^{9} (x) + C

Solution steps

\int \frac{cos ( x )}{sin ^{10} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{10}} d u

= \int \frac{1}{u ^{10}} d u

Apply the Power Rule

: - \frac{1}{9 u ^{9}}

= - \frac{1}{9 u ^{9}}

Substitute back

u = sin (x)

= - \frac{1}{9 sin ^{9} ( x )}

Simplify

- \frac{1}{9 sin ^{9} ( x )} : - \frac{1}{9} csc^{9} (x)

= - \frac{1}{9} csc^{9} (x)

Add a constant to the solution

= - \frac{1}{9} csc^{9} (x) + C

\int 4 t^{2} + 4 d t

\int sin (2 x + π) d x

\frac{d y}{d x} = \frac{e ^{x} - y}{x}

x \to 0 lim (x sin (\frac{1}{x}))

What is the integral of (cos(x))/(sin^{10)(x)} ?
The integral of (cos(x))/(sin^{10)(x)} is -1/9 csc^9(x)+C