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

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

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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

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \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}

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

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

x^{l o g_{5} (x)}

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

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