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.

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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.

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Which did you take as your 'u' and which as your 'dv'?
u = ln(t), du = 1/t (dt); dv = t^(1/2)dt, v = (2t^(3/2)/3)
your mistake seems to be in vdu

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\[\huge \int vdu = \frac 23\int t^{3/2 - 2/2}\] is that what you did?
yeah
which gets 2/3 * integral of sqrt t
OHHHHHHHHH
i see what i did wrong, i think i'll get the right answer, thanks
welcome

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