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First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int e^{\sqrt{x}} dx $

$v=e^{t}$ to get $2 \int t e^{t} d t=2 t e^{t}-2 \int e^{t} d t=2 t e^{t}-2 e^{t}+C=2 \sqrt{x} e^{\sqrt{x}}-2 e^{\sqrt{x}}+C$

Integration Techniques

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Oregon State University

Harvey Mudd College

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