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.

Question

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.

anonymous · Answer

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

anonymous · Answer

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

lgbasallote · Answer

your mistake seems to be in vdu

lgbasallote · Answer

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

anonymous · Answer

yeah

anonymous · Answer

which gets 2/3 * integral of sqrt t

anonymous · Answer

OHHHHHHHHH

anonymous · Answer

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

lgbasallote · Answer

welcome