Question

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

Answer 1

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

Answer 2

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

Answer 3

this looks trigonometric doesn't it?

Answer 4

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

Answer 5

exactly

Answer 6

but how do I get rid of the 64?

Answer 7

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 \[\Large 1+\tan^2\theta=\sec^2\theta \]

Answer 8

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

Answer 9

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