What is the integral of (-cos(x))/(sin^7(x)) ?

The integral of (-cos(x))/(sin^7(x)) is 1/6 csc^6(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^7(x))

\int \frac{- cos ( x )}{sin ^{7} ( x )} d x

\frac{1}{6} csc^{6} (x) + C

Solution steps

\int \frac{- cos ( x )}{sin ^{7} ( x )} d x

Take the constant out:

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

= - \int \frac{cos ( x )}{sin ^{7} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{7}} d u

= - \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= - (- \frac{1}{6 u ^{6}})

Substitute back

u = sin (x)

= - (- \frac{1}{6 sin ^{6} ( x )})

Simplify

- (- \frac{1}{6 sin ^{6} ( x )}) : \frac{1}{6} csc^{6} (x)

= \frac{1}{6} csc^{6} (x)

Add a constant to the solution

= \frac{1}{6} csc^{6} (x) + C

\int \frac{4 x + 3}{1 - 4 x ^{2}} d x

\int 8 x^{7} ln (x) d x

\int 5 x^{2} b^{7 x^{3}} d x

\int \frac{4}{5 x x ^{2} + 9} d x

\int 2 x (x^{2} + 3) d x

What is the integral of (-cos(x))/(sin^7(x)) ?
The integral of (-cos(x))/(sin^7(x)) is 1/6 csc^6(x)+C