Question

integral x^2 logx dx

Answer 1

parts

Answer 2

im thinking integration by parts...

let u = logx dv = x^2
du = 1/x v = (x^3)/3

\(\Huge \frac{x^3 logx}{3} - \int{}{} \frac{x^3}{3x}\)

Answer 3

can you fo the rest from there?

Answer 4

yeah i think so but what is the integral of just logx for reference?

Answer 5

\[\int\ln(x)dx=x\ln(x)-x+c\]

Answer 6

does that apply for common logs too or just nat logs

Answer 7

\[\log_a(x)=\frac{\ln(x)}{\ln(a)}\]

Answer 8

\[\int\log_a(x)dx=\int\frac{\ln(x)}{\ln(a)}dx=\frac{1}{\ln(a)}\int\ln(x)dx\]

Answer 9

thank you!