What is the integral of x^2+e^{x^3} ?

The integral of x^2+e^{x^3} is (x^3)/3+(-(x\Gamma(1/3 ,-x^3))/(3\sqrt[3]{-x^3)})+C

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integral of x^2+e^{x^3}

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

\frac{x ^{3}}{3} + (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

Solution steps

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

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

\int e^{x^{3}} d x = - \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}

= \frac{x ^{3}}{3} + (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}})

Add a constant to the solution

= \frac{x ^{3}}{3} + (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

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