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

The integral of 3*cos(x)+\sqrt[3]{x}+2 is 3sin(x)+3/4 x^{4/3}+2x+C

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integral of 3*cos(x)+\sqrt[3]{x}+2

\int 3 \cdot cos (x) + 3 x + 2 d x

3 sin (x) + \frac{3}{4} x^{\frac{4}{3}} + 2 x + C

Solution steps

\int 3 cos (x) + 3 x + 2 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 cos (x) d x + \int 3 x d x + \int 2 d x

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

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

\int 2 d x = 2 x

= 3 sin (x) + \frac{3}{4} x^{\frac{4}{3}} + 2 x

Add a constant to the solution

= 3 sin (x) + \frac{3}{4} x^{\frac{4}{3}} + 2 x + C

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What is the integral of 3*cos(x)+\sqrt[3]{x}+2 ?
The integral of 3*cos(x)+\sqrt[3]{x}+2 is 3sin(x)+3/4 x^{4/3}+2x+C