Question

integrate: (1+lnx)e^(xlnx) dx

Answer 1

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

Answer 2

e^(xlnx) +C

Answer 3

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

Answer 4

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

Answer 5

can u explain the steps?

Answer 6

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

Answer 7

thanx.. i really appreciate it