What is the integral of cos^3(x)(sin(x)) ?

The integral of cos^3(x)(sin(x)) is -(cos^4(x))/4+C

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integral of cos^3(x)(sin(x))

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

- \frac{cos ^{4} ( x )}{4} + C

Solution steps

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

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cos (x)

= - \frac{cos ^{4} ( x )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( x )}{4} + C

y = x^{2} - 8, y = 1

y = 5 e^{5 t + 1}

\frac{d}{d x} (ln (cos (x)) + x)

\int \frac{x ^{2}}{( 9 x ^{2} - 4 ) ^{\frac{5}{2}}} d x

\int_{0}^{π} (5 e^{x} + 3 sin (x)) d x

What is the integral of cos^3(x)(sin(x)) ?
The integral of cos^3(x)(sin(x)) is -(cos^4(x))/4+C