guys first timer here. cant quite figure this one out.
ʃ dt/ t√(5tē-3)
it looks to me to be a sec^-1u type of question but i cant seem to find the correct u value. any help from you smart peoples?
Since $\displaystyle t=\frac{\sqrt{3}}{\sqrt{5}}u$ and $\displaystyle dt = \frac{\sqrt{3}}{\sqrt{5}}\,du$, you have: $\displaystyle \int\frac{dt}{t\sqrt{5t^2-3}} = \int\frac{\frac{\sqrt{3}}{\sqrt{5}}\,du}{\frac{\sq rt{3}}{\sqrt{5}}u\sqrt{3(u^2-1)}}$ $\displaystyle = \frac{1}{\sqrt{3}}\int\frac{du}{u\sqrt{u^2-1}}$
Spoiler: