What is the integral of 9sin^5(x)cos(x) ?

The integral of 9sin^5(x)cos(x) is 3/2 sin^6(x)+C

Popular >

integral of 9sin^5(x)cos(x)

\int 9 sin^{5} (x) cos (x) d x

\frac{3}{2} sin^{6} (x) + C

Solution steps

\int 9 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

= 9 \cdot \int sin^{5} (x) cos (x) d x

Apply u-substitution

: \int u^{5} d u

= 9 \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 9 \cdot \frac{u ^{6}}{6}

Substitute back

u = sin (x)

= 9 \cdot \frac{sin ^{6} ( x )}{6}

Simplify

9 \cdot \frac{sin ^{6} ( x )}{6} : \frac{3}{2} sin^{6} (x)

= \frac{3}{2} sin^{6} (x)

Add a constant to the solution

= \frac{3}{2} sin^{6} (x) + C

\int (3 x^{2} + 4)^{2} d x

\int (x^{3} + 1) cos (x^{4} + 4 x) d x

\int \frac{1}{x ^{6} + x ^{4}} d x

\int \frac{arctan ( x )}{( 1 + x ^{2} )} d x

\int cos^{2} (ω t + φ) d t

What is the integral of 9sin^5(x)cos(x) ?
The integral of 9sin^5(x)cos(x) is 3/2 sin^6(x)+C