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

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

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

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

\frac{sin ^{4} ( x )}{4} + C

Solution steps

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

Simplify

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

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

y = 5 x^{2}

\int_{- 1}^{1} - x d x

\int_{- 5}^{5} ∣ x ∣ d x

f (x) = - 2 x^{2} + 3

x^{^{''}} - 5 x = 0

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