What is the integral of sin(8x)\sqrt[3]{cos(8x)} ?

The integral of sin(8x)\sqrt[3]{cos(8x)} is -3/32 cos^{4/3}(8x)+C

Popular >

integral of sin(8x)\sqrt[3]{cos(8x)}

- \frac{3}{32} cos^{\frac{4}{3}} (8 x) + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (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} v^{\frac{4}{3}}

= \frac{1}{8} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= \frac{1}{8} (- \frac{3}{4} cos^{\frac{4}{3}} (8 x))

Simplify

\frac{1}{8} (- \frac{3}{4} cos^{\frac{4}{3}} (8 x)) : - \frac{3}{32} cos^{\frac{4}{3}} (8 x)

= - \frac{3}{32} cos^{\frac{4}{3}} (8 x)

Add a constant to the solution

= - \frac{3}{32} cos^{\frac{4}{3}} (8 x) + C

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

f (x) = 4^{x} - x^{2} + 3 ln (x)

\frac{40 t ^{2}}{t ^{2} + 150}

x \to 0 + lim (\frac{3}{x} - \frac{2}{ln ( x )})

\int \frac{- 1}{x ^{3}} d x

What is the integral of sin(8x)\sqrt[3]{cos(8x)} ?
The integral of sin(8x)\sqrt[3]{cos(8x)} is -3/32 cos^{4/3}(8x)+C