What is the integral of 5sin^3(x)cos(x) ?

The integral of 5sin^3(x)cos(x) is 5/4 sin^4(x)+C

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integral of 5sin^3(x)cos(x)

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

\frac{5}{4} sin^{4} (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u^{3} d u

= 5 \cdot \int u^{3} d u

Apply the Power Rule

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

= 5 \cdot \frac{u ^{4}}{4}

Substitute back

u = sin (x)

= 5 \cdot \frac{sin ^{4} ( x )}{4}

Simplify

5 \cdot \frac{sin ^{4} ( x )}{4} : \frac{5}{4} sin^{4} (x)

= \frac{5}{4} sin^{4} (x)

Add a constant to the solution

= \frac{5}{4} sin^{4} (x) + C

\frac{d}{d x} ((3 - x) (2 x^{2} - x))

e^{t} cos (t) - e^{t} sin (t)

\int \frac{1 - x}{x ^{2} + 1} d x

\frac{\partial}{\partial x} (ln (x + y))

y^{^{'}} = e^{(y - x)}

What is the integral of 5sin^3(x)cos(x) ?
The integral of 5sin^3(x)cos(x) is 5/4 sin^4(x)+C