What is the integral of e^{y^3} ?

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

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integral of e^{y^3}

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

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

Solution steps

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

Use the nonelementary integral:

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

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

Add a constant to the solution

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

\frac{d}{d x} (r (x) (x)^{2} e^{r (x) x})

2 y^{^{''}} + 2 y^{^{'}} + y = 0

\frac{\partial}{\partial y} (\frac{x - y}{x})

\int 3 x e^{3 z} + 5 d z

\frac{( s - 1 ) ^{3}}{s ^{4}}

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