What is the integral of 7sin^5(x)cos(x) ?

The integral of 7sin^5(x)cos(x) is 7/6 sin^6(x)+C

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integral of 7sin^5(x)cos(x)

\int 7 sin^{5} (x) cos (x) d x

\frac{7}{6} sin^{6} (x) + C

Solution steps

\int 7 sin^{5} (x) cos (x) d x

Take the constant out:

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

= 7 \cdot \int sin^{5} (x) cos (x) d x

Apply u-substitution

= 7 \cdot \int u^{5} d u

Apply the Power Rule

= 7 \cdot \frac{u ^{6}}{6}

Substitute back

u = sin (x)

= 7 \cdot \frac{sin ^{6} ( x )}{6}

Simplify

7 \cdot \frac{sin ^{6} ( x )}{6} : \frac{7}{6} sin^{6} (x)

= \frac{7}{6} sin^{6} (x)

Add a constant to the solution

= \frac{7}{6} sin^{6} (x) + C

What is the integral of 7sin^5(x)cos(x) ?
The integral of 7sin^5(x)cos(x) is 7/6 sin^6(x)+C