What is the integral of x^{13}e^{x^{14}} ?

The integral of x^{13}e^{x^{14}} is 1/14 e^{x^{14}}+C

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integral of x^{13}e^{x^{14}}

\int x^{13} e^{x^{14}} d x

\frac{1}{14} e^{x^{14}} + C

Solution steps

\int x^{13} e^{x^{14}} d x

Apply u-substitution

: \int \frac{1}{14} d u

= \int \frac{1}{14} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{14} u

Substitute back

u = e^{x^{14}}

= \frac{1}{14} e^{x^{14}}

Add a constant to the solution

= \frac{1}{14} e^{x^{14}} + C

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What is the integral of x^{13}e^{x^{14}} ?
The integral of x^{13}e^{x^{14}} is 1/14 e^{x^{14}}+C