stuck on an integral, should be simple but I'm not seeing what substitution to make....

Question

anonymous · Answer

$$8 \pi \int\limits_{0}^{1} e ^{2y} \sqrt (1+64e ^{4y})dy$$

anonymous · Answer

should I do u=e^(2y)?

anonymous · Answer

this looks trigonometric doesn't it?

anonymous · Answer

because of the sqrt(a+x^2)?

anonymous · Answer

exactly

anonymous · Answer

but how do I get rid of the 64?

anonymous · Answer

I am not yet sure if I make the integral worse than it has to be, to be honest with you. But consider the following substitution:

$$\Large e^{2y}=\frac{1}{8}\tan\theta $$

You know that $$\Large 1+\tan^2\theta=\sec^2\theta $$

anonymous · Answer

okay I'll try that. I have to run but I'll attempt it later. Thanks again!

anonymous · Answer

but I am not yet certain if that makes the integral any better.