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

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

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integral of (e^x-x^2+2/(\sqrt[3]{x)})

\int (e^{x} - x^{2} + \frac{2}{3 x}) d x

e^{x} - \frac{x ^{3}}{3} + 3 x^{\frac{2}{3}} + C

Solution steps

\int e^{x} - x^{2} + \frac{2}{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 e^{x} d x - \int x^{2} d x + \int \frac{2}{3 x} d x

\int e^{x} d x = e^{x}

\int x^{2} d x = \frac{x ^{3}}{3}

\int \frac{2}{3 x} d x = 3 x^{\frac{2}{3}}

= e^{x} - \frac{x ^{3}}{3} + 3 x^{\frac{2}{3}}

Add a constant to the solution

= e^{x} - \frac{x ^{3}}{3} + 3 x^{\frac{2}{3}} + C

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