What is the integral of e^{y^4} ?

The integral of e^{y^4} is -(y\Gamma(1/4 ,-y^4))/(4\sqrt[4]{-y^4)}+C

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integral of e^{y^4}

\int e^{y^{4}} d y

- \frac{y Γ ( \frac{1}{4} , - y ^{4} )}{4 4 - y ^{4}} + C

Solution steps

\int e^{y^{4}} 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}{4} , - y ^{4} )}{4 4 - y ^{4}}

Add a constant to the solution

= - \frac{y Γ ( \frac{1}{4} , - y ^{4} )}{4 4 - y ^{4}} + C

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What is the integral of e^{y^4} ?
The integral of e^{y^4} is -(y\Gamma(1/4 ,-y^4))/(4\sqrt[4]{-y^4)}+C