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

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

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

\int (3 x + cos (3 x)) d x

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

Solution steps

\int 3 x + cos (3 x) d x

Apply the Sum Rule:

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

= \int 3 x d x + \int cos (3 x) d x

\int 3 x d x = \frac{3}{4} x^{\frac{4}{3}}

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

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

Add a constant to the solution

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

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