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

The integral of (cos(t))/(sin^7(t)) is -1/6 csc^6(t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(t))/(sin^7(t))

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

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

Solution steps

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

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 (t)

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

Simplify

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

= - \frac{1}{6} csc^{6} (t)

Add a constant to the solution

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

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

\int (5 x + 6)^{4} d x

\int y - 2 d y

\int \frac{x}{x x ^{2} - 1} d x

\int cos (8 x) (10 + sin (8 x))^{6} d x

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