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

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

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integral of (\sqrt[3]{x}-sin(x))

\frac{3}{4} x^{\frac{4}{3}} + cos (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 (x) d x = - cos (x)

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

Simplify

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

Add a constant to the solution

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

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