What is the integral of sin(16x)\sqrt[3]{cos(16x)} ?

The integral of sin(16x)\sqrt[3]{cos(16x)} is -3/64 cos^{4/3}(16x)+C

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integral of sin(16x)\sqrt[3]{cos(16x)}

- \frac{3}{64} cos^{\frac{4}{3}} (16 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}{16} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= \frac{1}{16} (- \frac{3}{4} cos^{\frac{4}{3}} (16 x))

Simplify

\frac{1}{16} (- \frac{3}{4} cos^{\frac{4}{3}} (16 x)) : - \frac{3}{64} cos^{\frac{4}{3}} (16 x)

= - \frac{3}{64} cos^{\frac{4}{3}} (16 x)

Add a constant to the solution

= - \frac{3}{64} cos^{\frac{4}{3}} (16 x) + C

\frac{d}{d x} (\frac{2 x}{2 x + 1})

f (x) = ln (1 - 3 x)

\int_{0}^{N} e^{(- s t)} sin (5 t) d t

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

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

What is the integral of sin(16x)\sqrt[3]{cos(16x)} ?
The integral of sin(16x)\sqrt[3]{cos(16x)} is -3/64 cos^{4/3}(16x)+C