What is the integral of \sqrt[3]{1-4sin(x)}*cos(x) ?

The integral of \sqrt[3]{1-4sin(x)}*cos(x) is -3/16 (1-4sin(x))^{4/3}+C

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integral of \sqrt[3]{1-4sin(x)}*cos(x)

- \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}} + 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 the Power Rule

= - \frac{1}{4} \cdot \frac{3}{4} v^{\frac{4}{3}}

Substitute back

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

Simplify

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

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

Add a constant to the solution

= - \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}} + C

What is the integral of \sqrt[3]{1-4sin(x)}*cos(x) ?
The integral of \sqrt[3]{1-4sin(x)}*cos(x) is -3/16 (1-4sin(x))^{4/3}+C