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

The integral of cos(t)sin^7(t) is (sin^8(t))/8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{sin ^{8} ( t )}{8} + C

Solution steps

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

Apply u-substitution

= \int u^{7} d u

Apply the Power Rule

= \frac{u ^{8}}{8}

Substitute back

u = sin (t)

= \frac{sin ^{8} ( t )}{8}

Add a constant to the solution

= \frac{sin ^{8} ( t )}{8} + C

\frac{d y}{d x} - y = e^{2 x}

\frac{d}{d x} (\frac{x ^{2}}{3 + 4 x})

d er i v a t i v e x^{l o g_{5} (x)}

\frac{\partial}{\partial x} (\frac{8}{x ^{2} + y ^{2}})

\frac{d}{d x} (\frac{1}{x + x ^{- 1}})

What is the integral of cos(t)sin^7(t) ?
The integral of cos(t)sin^7(t) is (sin^8(t))/8+C