What is the integral of 200sin(5x)\sqrt[3]{cos(5x)} ?

The integral of 200sin(5x)\sqrt[3]{cos(5x)} is -30cos^{4/3}(5x)+C

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integral of 200sin(5x)\sqrt[3]{cos(5x)}

- 30 cos^{\frac{4}{3}} (5 x) + C

Solution steps

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 u-substitution

Take the constant out:

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

Apply the Power Rule

= 200 \cdot \frac{1}{5} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= 200 \cdot \frac{1}{5} (- \frac{3}{4} cos^{\frac{4}{3}} (5 x))

Simplify

200 \cdot \frac{1}{5} (- \frac{3}{4} cos^{\frac{4}{3}} (5 x)) : - 30 cos^{\frac{4}{3}} (5 x)

= - 30 cos^{\frac{4}{3}} (5 x)

Add a constant to the solution

= - 30 cos^{\frac{4}{3}} (5 x) + C

What is the integral of 200sin(5x)\sqrt[3]{cos(5x)} ?
The integral of 200sin(5x)\sqrt[3]{cos(5x)} is -30cos^{4/3}(5x)+C