What is the integral from-1 to 1 of x^4e^{x^5} ?

The integral from-1 to 1 of x^4e^{x^5} is e/5-1/(5e)

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integral from-1 to 1 of x^4e^{x^5}

\int_{- 1}^{1} x^{4} e^{x^{5}} d x

\frac{e}{5} - \frac{1}{5 e}

Decimal Notation

0.47008 \dots

Solution steps

\int_{- 1}^{1} x^{4} e^{x^{5}} d x

Apply Integration By Parts

: [\frac{1}{5} e^{x^{5}} x^{5} - \int e^{x^{5}} x^{9} d x]_{- 1}^{1}

= [\frac{1}{5} e^{x^{5}} x^{5} - \int e^{x^{5}} x^{9} d x]_{- 1}^{1}

\int e^{x^{5}} x^{9} d x = \frac{1}{5} (e^{x^{5}} x^{5} - e^{x^{5}})

= [\frac{1}{5} e^{x^{5}} x^{5} - \frac{1}{5} (e^{x^{5}} x^{5} - e^{x^{5}})]_{- 1}^{1}

Simplify

[\frac{1}{5} e^{x^{5}} x^{5} - \frac{1}{5} (e^{x^{5}} x^{5} - e^{x^{5}})]_{- 1}^{1} : [\frac{1}{5} e^{x^{5}}]_{- 1}^{1}

= [\frac{1}{5} e^{x^{5}}]_{- 1}^{1}

Compute the boundaries:

\frac{e}{5} - \frac{1}{5 e}

= \frac{e}{5} - \frac{1}{5 e}

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What is the integral from-1 to 1 of x^4e^{x^5} ?
The integral from-1 to 1 of x^4e^{x^5} is e/5-1/(5e)