anonymous 5 years ago when integrating radt times lnt by parts should u be lnt or rad t?

1. amistre64

thats a little tooooo cryptic, can you english it up some?

2. amistre64

sqrt(t).ln(t) perhaps?

3. watchmath

$$u=\ln t$$

4. amistre64

LN(t) looks alot like int

5. anonymous

$\int\limits_{1}^{\sqrt{5}}\sqrt{t}lnt$dt

6. watchmath

Here is a trick that most of the time worsk. Use I L A T E for choosing u. I(inverse), L(og), A(lgebraic), T(rig), E(xp). In your problem you have A(lgebraic) and L(og). Since L come first before A. Choose L as your u. To learn more look at here: http://www.youtube.com/watch?v=cdLF-_gymRI

7. anonymous

ok thanks...so lets say dv=lntdt. what is v then? the antiderivative of lnt i mean?

8. watchmath

Well $$\sqrt{t}$$ is algebraic. So we choose L which is $$u=\ln t$$ and $$dv=\sqrt{t}dt$$

9. anonymous

tlnt-t is the integral of lnt. To find that, you need to use by parts