The question asks for the integral of $e^{mx^{3}}.$ How do I calculate the antiderivative of a function that has $e^{x^{3}}$ lets say. I want to make sure I know how to take the antiderivative of exponential functions.
2026-04-07 07:27:05.1775546825
Integral of $e^{mx^{3}}$
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Let $mt^3=-u,$
$$\int_0^xe^{mt^3}\ dt=-\int_0^{mx^3}\frac1{3\sqrt[3]{mu}}e^{-u}\ du=-\frac1{3\sqrt[3]{m}}\gamma\left(\frac23,mx^3\right)$$
where $\gamma(a,b)$ is the lower incomplete gamma function.