What is the integral of cos^1(x)sin^4(x) ?

The integral of cos^1(x)sin^4(x) is (sin^5(x))/5+C

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integral of cos^1(x)sin^4(x)

\int cos^{1} (x) sin^{4} (x) d x

\frac{sin ^{5} ( x )}{5} + C

Solution steps

\int cos^{1} (x) sin^{4} (x) d x

Simplify

sin^{4} (x) : sin^{3} (x) sin (x)

= \int cos^{1} (x) sin^{3} (x) sin (x) d x

Simplify

cos^{1} (x) sin^{3} (x) sin (x) : sin^{4} (x) cos (x)

= \int sin^{4} (x) cos (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = sin (x)

= \frac{sin ^{5} ( x )}{5}

Add a constant to the solution

= \frac{sin ^{5} ( x )}{5} + C

\int 1 0^{5 x} d x

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\int 2^{x} 3^{2 x} d x

\int 3 sin (2 x) cos^{5} (2 x) d x

What is the integral of cos^1(x)sin^4(x) ?
The integral of cos^1(x)sin^4(x) is (sin^5(x))/5+C