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

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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