What is the integral of e^{t^7} ?

The integral of e^{t^7} is -(t\Gamma(1/7 ,-t^7))/(7\sqrt[7]{-t^7)}+C

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integral of e^{t^7}

\int e^{t^{7}} d t

- \frac{t Γ ( \frac{1}{7} , - t ^{7} )}{7 7 - t ^{7}} + C

Solution steps

\int e^{t^{7}} d t

Use the nonelementary integral:

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

= - \frac{t Γ ( \frac{1}{7} , - t ^{7} )}{7 7 - t ^{7}}

Add a constant to the solution

= - \frac{t Γ ( \frac{1}{7} , - t ^{7} )}{7 7 - t ^{7}} + C

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What is the integral of e^{t^7} ?
The integral of e^{t^7} is -(t\Gamma(1/7 ,-t^7))/(7\sqrt[7]{-t^7)}+C