How do you integrate $x^4 e^x^5 dx$ ?

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Answer 1 · 2015-04-17T16:18:06

$int x^4e^(x^5) dx$

Use substitution to write this an an integral of $e^u du$

Let $u = x^5$ . This makes $du = 5x^4 dx$ ,

$int x^4e^(x^5) dx = 1/5 int e^(x^5)(5x^4) dx = 1/5 int e^u du$

$=1/5 e^u +C = 1/5 e^(x^5) +C$

(Check by differentiating $1/5 e^(x^5) +C$ )

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