What is the integral of 5sin^4(x)cos(x) ?

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

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integral of 5sin^4(x)cos(x)

\int 5 sin^{4} (x) cos (x) d x

sin^{5} (x) + C

Solution steps

\int 5 sin^{4} (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^{4} (x) cos (x) d x

Apply u-substitution

= 5 \cdot \int u^{4} d u

Apply the Power Rule

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

Substitute back

u = sin (x)

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

Simplify

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

= sin^{5} (x)

Add a constant to the solution

= sin^{5} (x) + C

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