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

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

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

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

- \frac{cos ^{5} ( x )}{5} + C

Solution steps

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

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

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

= - \int u^{4} d u

Apply the Power Rule

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

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

Substitute back

u = cos (x)

= - \frac{cos ^{5} ( x )}{5}

Add a constant to the solution

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

\int (x^{2} + 1) (x^{3} + 3 x)^{4} d x

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

f (x) = 7 + 5 x

y^{^{'}} = k \cdot y

\frac{( 3 t - 1 )}{t - 2}

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