What is the integral of 224sin(7x)\sqrt[3]{cos(7x)} ?

The integral of 224sin(7x)\sqrt[3]{cos(7x)} is -24cos^{4/3}(7x)+C

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integral of 224sin(7x)\sqrt[3]{cos(7x)}

- 24 cos^{\frac{4}{3}} (7 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

: \frac{3}{4} v^{\frac{4}{3}}

= 224 \cdot \frac{1}{7} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= 224 \cdot \frac{1}{7} (- \frac{3}{4} cos^{\frac{4}{3}} (7 x))

Simplify

224 \cdot \frac{1}{7} (- \frac{3}{4} cos^{\frac{4}{3}} (7 x)) : - 24 cos^{\frac{4}{3}} (7 x)

= - 24 cos^{\frac{4}{3}} (7 x)

Add a constant to the solution

= - 24 cos^{\frac{4}{3}} (7 x) + C

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What is the integral of 224sin(7x)\sqrt[3]{cos(7x)} ?
The integral of 224sin(7x)\sqrt[3]{cos(7x)} is -24cos^{4/3}(7x)+C