What is the integral of e^{-x^4} ?

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

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integral of e^{-x^4}

\int e^{- x^{4}} d x

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

Solution steps

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (- 2 x y z^{2} + 12)

10 sin (6 t)

\int \frac{x}{x - x ^{2}} d x

k = 2 \sum \infty (\frac{1}{3})^{k}

y = arcsin (x) + 1 - x^{2}

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