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

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

Popular >

integral of cos^3(2θ)sin(2θ)

\int cos^{3} (2 θ) sin (2 θ) d θ

- \frac{1}{8} cos^{4} (2 θ) + C

Solution steps

\int cos^{3} (2 θ) sin (2 θ) d θ

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 = cos^{3} (2 θ)

= - \frac{1}{6} \cdot \frac{3}{4} (cos^{3} (2 θ))^{\frac{4}{3}}

Simplify

- \frac{1}{6} \cdot \frac{3}{4} (cos^{3} (2 θ))^{\frac{4}{3}} : - \frac{1}{8} cos^{4} (2 θ)

= - \frac{1}{8} cos^{4} (2 θ)

Add a constant to the solution

= - \frac{1}{8} cos^{4} (2 θ) + C

\int 5 e^{x} cos^{2} (x) d x

\int y^{2} (3 - y^{3})^{\frac{2}{3}} d y

\int x \cdot x^{2} + 1 d x

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

x \to \infty lim (- (e^{x}))

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