What is the integral of sin(4x)cos^3(4x) ?

The integral of sin(4x)cos^3(4x) is -1/16 cos^4(4x)+C

Popular >

integral of sin(4x)cos^3(4x)

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

- \frac{1}{16} cos^{4} (4 x) + C

Solution steps

\int sin (4 x) cos^{3} (4 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}{12} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = cos^{3} (4 x)

= - \frac{1}{12} \cdot \frac{3}{4} (cos^{3} (4 x))^{\frac{4}{3}}

Simplify

- \frac{1}{12} \cdot \frac{3}{4} (cos^{3} (4 x))^{\frac{4}{3}} : - \frac{1}{16} cos^{4} (4 x)

= - \frac{1}{16} cos^{4} (4 x)

Add a constant to the solution

= - \frac{1}{16} cos^{4} (4 x) + C

\int \frac{( arctan ( 7 x ) )}{1 + 49 x ^{2}} d x

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

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

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

\int \frac{4 x ^{2}}{x ^{2} + 1} d x

What is the integral of sin(4x)cos^3(4x) ?
The integral of sin(4x)cos^3(4x) is -1/16 cos^4(4x)+C