## jaersyn Group Title integration by parts question. what is the indefinite integral of sqrt(t)ln(t)dt? I got (2/3)(t^(3/2))(ln(t) - 1) + C but the answer key says (2/9)(t^(3/2))(3ln(t) - 2) + C Sorry for lack of symbols, I know it's hard to read. one year ago one year ago

1. CliffSedge Group Title

Which did you take as your 'u' and which as your 'dv'?

2. jaersyn Group Title

u = ln(t), du = 1/t (dt); dv = t^(1/2)dt, v = (2t^(3/2)/3)

3. lgbasallote Group Title

your mistake seems to be in vdu

4. lgbasallote Group Title

$\huge \int vdu = \frac 23\int t^{3/2 - 2/2}$ is that what you did?

5. jaersyn Group Title

yeah

6. jaersyn Group Title

which gets 2/3 * integral of sqrt t

7. jaersyn Group Title

OHHHHHHHHH

8. jaersyn Group Title

i see what i did wrong, i think i'll get the right answer, thanks

9. lgbasallote Group Title

welcome