Question

Find the integral of t/(sqrt(2t^2-1)) dt. (Answer: (1/2)*sqrt(2t^2-1)+C)

Answer 1

I believe you need to do some substitution. I'll try my best to put it in the equation form:
\[\int\limits \frac{t}{\sqrt{2t^2-1}}dt\]
Let \(u=2t^2-1\). Then, \(du=4t~dt\). If we solve for \(dt\), we get \(dt=\frac{1}{4t} du\). Substituting for \(dt\), we get: \[\int\limits \frac{t}{\sqrt{u}}\frac{1}{4t}du\]
Can you solve it from here?

Answer 2

Thank you.

Answer 3

Anytime.