## anonymous 5 years ago integrate: (1+lnx)e^(xlnx) dx

1. anonymous

$\int\limits_{}^{}(1+\ln x)e^{x lnx}$

2. amistre64

e^(xlnx) +C

3. amistre64

[S] Du e^u du -> e^u

4. amistre64

D(x ln(x)) = 1+ln(x) :)

5. anonymous

can u explain the steps?

6. amistre64

integration is not s step procedure; it is an art form. The best thing to do is to realize that (1+ln(x)) is the derivative of x ln(x). We should know by now that the derivative of e^u = Du e^u so to suit it back up we just revert it to e^u again..... You have the structure Du e^u... so the answer is simply e^u; with u=xlnx

7. anonymous

thanx.. i really appreciate it