What is the integral of sin^3(2x)cos(2x) ?

The integral of sin^3(2x)cos(2x) is 1/8 sin^4(2x)+C

Popular >

integral of sin^3(2x)cos(2x)

\int sin^{3} (2 x) cos (2 x) d x

\frac{1}{8} sin^{4} (2 x) + C

Solution steps

\int sin^{3} (2 x) cos (2 x) d x

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= \frac{1}{6} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = sin^{3} (2 x)

= \frac{1}{6} \cdot \frac{3}{4} (sin^{3} (2 x))^{\frac{4}{3}}

Simplify

\frac{1}{6} \cdot \frac{3}{4} (sin^{3} (2 x))^{\frac{4}{3}} : \frac{1}{8} sin^{4} (2 x)

= \frac{1}{8} sin^{4} (2 x)

Add a constant to the solution

= \frac{1}{8} sin^{4} (2 x) + C

\int \frac{6}{x ^{2} + 16} d x

y^{^{''}} - 8 y^{^{'}} + 15 y = 0, y (0) = 1, y^{^{'}} (0) = 4

\frac{d y}{d t} + y = 2, y (0) = 0

\int cos^{4} (θ) sin (θ) d θ

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

What is the integral of sin^3(2x)cos(2x) ?
The integral of sin^3(2x)cos(2x) is 1/8 sin^4(2x)+C