Integration

[tylerl]

Find the integral.

integral of y^ln(y) dy

The sections are for substitution and integration by parts. First of all I am having a hard time figuring out which one I should use and secondly, I have tried to use both and cannot figure what to sub for u or what to use as u and v' if I tried to use integration by parts.

 

[galactus]

This one may pose a problem because it is not doable by elelmentary means, such as part,s substitution, etc.

It is the same as \(\displaystyle \int e^{(ln(x))^{2}}dx\), which has no nice indefinite form.

It's indefinite form will involve the 'error function'. Here is what Wolfram alpha gave:

\(\displaystyle \frac{\sqrt{\pi}\text{erfi}(ln(x)+\frac{1}{2})}{2\sqrt[4]{e}}+C\)

Are you sure you copied it correctly.