What is the integral of e^{sqrt(x^3)} ?

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

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integral of e^{sqrt(x^3)}

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

- \frac{x Γ ( \frac{1}{\frac{3}{2}} , - x ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - x ^{\frac{3}{2}}} + C

Solution steps

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

x^{3} = x^{\frac{3}{2}},

assuming

x \geq 0

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

Use the nonelementary integral:

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

= - \frac{x Γ ( \frac{1}{\frac{3}{2}} , - x ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - x ^{\frac{3}{2}}}

Add a constant to the solution

= - \frac{x Γ ( \frac{1}{\frac{3}{2}} , - x ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - x ^{\frac{3}{2}}} + C

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