What is the integral of [\sqrt[3]{x^2}+sin(3x)] ?

The integral of [\sqrt[3]{x^2}+sin(3x)] is 3/5 x^{5/3}-1/3 cos(3x)+C

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integral of [\sqrt[3]{x^2}+sin(3x)]

\frac{3}{5} x^{\frac{5}{3}} - \frac{1}{3} cos (3 x) + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

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

Add a constant to the solution

= \frac{3}{5} x^{\frac{5}{3}} - \frac{1}{3} cos (3 x) + C

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What is the integral of [\sqrt[3]{x^2}+sin(3x)] ?
The integral of [\sqrt[3]{x^2}+sin(3x)] is 3/5 x^{5/3}-1/3 cos(3x)+C