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I'm trying to use integration by parts here for this integral:

$$ I = \frac{1}{2 e^{\sqrt{x}}- \lambda x }dx$$

So far, I get

$$u=\sqrt{x}$$, and $$dv = \frac{1}{2\sqrt{x}} dx$$

and I'm not sure what I do next...

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    You are using an u-substitution, not integration by parts. – 2017-02-26
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    This integral cannot be expressed in terms of standard mathematical functions – 2017-02-26
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    I assume you mean there is no closed form for the integral. – 2017-02-26

1 Answers 1

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As you have written it, your integrand is not of the form $u\ dv$ for the $u, dv$ you have specified, so the integration by parts will not work. With that $u$ there is no sensible $dv$ that you can specify. You could use $u=\frac{1}{2 e^{\sqrt{x}}- \lambda x }, dv=dx$ but I do not expect that to lead to progress as $du$ is no simpler.

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    I see what you are saying. Thanks. – 2017-02-26