Question

integration by parts
1. Integral [(x-1)ln(x)]
2. Integral [(sqrt (x) )ln(x)]

Answer 1

ok..first what will u choose to differentiate

Answer 2

that is what will be your f(x)?

Answer 3

i did u = ln(x) and dv = x-1. Is that right?

Answer 4

that's right, what you have got?

Answer 5

for 1 I got ln(x)(x^2/2) -x^2/4?

Answer 6

for 2 I got lnx(2/3)(x^3/2)- 4/9(x^3/2)

Answer 7

check your calculations once again, I think you've made some little mistakes

Answer 8

I did but I can't find them... Can you walk me through

Answer 9

ok, for the first one u=ln x and dv=(x-1) dx

leads to du=\(\frac{dx}{x}\) and v=((x-1)^2)/2 and\[\int (x-1) \ln(x) dx=\frac{(x-1)^2}{2}\ln(x)-\int \frac{(x-1)^2}{2} \frac{dx}{x} \\ =\frac{(x-1)^2}{2}\ln(x)-\frac{1}{2} \int (x-2+\frac{1}{x}) dx=\frac{(x-1)^2}{2}\ln(x)-\frac{1}{2}(x^2-2x+\ln(x))+C\]

Answer 10

answer for the second is\[\frac{2}{9} x^{3/2}(-2+3\ln(x))+C\]