u-sub integration help

**lj212** · April 29th 2009, 03:13 PM

guys first timer here. cant quite figure this one out.

ʃ dt/ t√(5t²-3)

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?

**Danny** · April 29th 2009, 03:21 PM

Originally Posted by lj212

guys first timer here. cant quite figure this one out.

ʃ dt/ t√(5t²-3)

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?

$<br /> 5t^2 - 3 = 3 \left(\frac{5}{3}t^2 - 1 \right) = 3 \left( \left(\frac{\sqrt{5}}{\sqrt{3}} t\right)^2 - 1\right)<br />$ and $u = \frac{\sqrt{5}}{\sqrt{3}} t$

**redsoxfan325** · April 29th 2009, 03:43 PM

Originally Posted by danny arrigo

$<br /> 5t^2 - 3 = 3 \left(\frac{5}{3}t^2 - 1 \right) = 3 \left( \left(\frac{\sqrt{5}}{\sqrt{3}} t\right)^2 - 1\right)<br />$ and $u = \frac{\sqrt{5}}{\sqrt{3}} t$

Since $t=\frac{\sqrt{3}}{\sqrt{5}}u$ and $dt = \frac{\sqrt{3}}{\sqrt{5}}\,du$ , you have: $\int\frac{dt}{t\sqrt{5t^2-3}} = \int\frac{\frac{\sqrt{3}}{\sqrt{5}}\,du}{\frac{\sq rt{3}}{\sqrt{5}}u\sqrt{3(u^2-1)}}$ $= \frac{1}{\sqrt{3}}\int\frac{du}{u\sqrt{u^2-1}}$

Spoiler:

Thread: u-sub integration help

LinkBack

Thread Tools

Display

u-sub integration help

Similar Math Help Forum Discussions

Integration help please these are three small even basic integration problems

sketch the region of integration and change the order of integration.

Definite Integration - Double integration by parts

Simple Integration problem: Trigonometric Integration

Tricky integration, possibly Integration Factor

Search Tags