x*e^(3 lnx): How to solve this integration problem?

[Ekram]

Hello everyone,

I would like help in solving this calculus problem which is integrating x*e^(3 lnx). Please help me solve this problem, Thank you.

 

[stapel]

...[integrate] x*e^(3 lnx).

Please help me solve this problem.

We can't help until we can see where you're getting stuck. Assuming the exercise was something like this:

. . . . .\(\displaystyle \mbox{Integrate }\, \)$\displaystyle \displaystyle \int\, x\, e^{3\, \ln(x)}\, dx$

...what did you try first? How far did you get? Where did things bog down? For instance, you first applied a log rule (here) to simplify (or condense) the exponent. Then you simplified the whole second factor by applying a special instance (not quite "cancelling", but close: here) of "The Relationship" between logs and exponentials. You then multiplied the two polynomial terms. (...all of which was just algebra.) Then you applied the Power Rule (here) for integrals. And... then what?

When you reply, please include recent topics of study (u-substitution, numerical methods, etc), so we have a pretty good idea of what you're probably supposed to be doing. If this exercise came from a particular section in your textbook (rather than the chapter review or some other source), please include the topic of that section. Thank you!

 

[Deleted member 4993]

Hello everyone,

I would like help in solving this calculus problem which is integrating x*e^(3 lnx). Please help me solve this problem, Thank you.

hint:...e^[ln(a)] = a