How can I integrate the composite root integral \int\sqrt{40t^2+e^t^2}dt?

[naphiefx]

Homework Statement
\int\sqrt{40t^2+e^t^2}dt

That should be e^t^2.
How would I go about doing this?

 

[Cyosis]

You can forget about a primitive in terms of elementary functions. It doesn't exist as is the case in most situations. What you could try is to write the integrand as a series expansion and integrate term by term.

 

[Mark44]

You can forget about a primitive in terms of elementary functions. It doesn't exist as is the case in most situations. What you could try is to write the integrand as a series expansion and integrate term by term.

That's generally good advice, but the square root in this case is going to complicate this strategy a lot!