1. ## integral of xlogx

Hey all,

i follow my notes from class to integrate x logx dx

and i come up with the answer 1 - log x,

however when i check my answer with Wolframs online integrator, it gets a different answer.

can somebody show me step by step how to do it?

heres what i did,

x logx dx

= x * 1/x - "int" 1/x * 1

= 1 - logx

our class example doesnt have the x on the front, it just has log x dx.

thanks for any help,

Mitch

2. Originally Posted by Mitch281008
Hey all,

i follow my notes from class to integrate x logx dx

and i come up with the answer 1 - log x,

however when i check my answer with Wolframs online integrator, it gets a different answer.

can somebody show me step by step how to do it?

heres what i did,

x logx dx

= x * 1/x - "int" 1/x * 1

= 1 - logx

our class example doesnt have the x on the front, it just has log x dx.

thanks for any help,

Mitch
hi

try integration by parts .

$\displaystyle \int x\ln x dx$

$\displaystyle =\ln x\int x dx-\int [\int x dx]\frac{1}{x}dx$

$\displaystyle =\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+c$

3. Originally Posted by Mitch281008
Hey all,

i follow my notes from class to integrate x logx dx

and i come up with the answer 1 - log x,

however when i check my answer with Wolframs online integrator, it gets a different answer.

can somebody show me step by step how to do it?

heres what i did,

x logx dx

= x * 1/x - "int" 1/x * 1

= 1 - logx

our class example doesnt have the x on the front, it just has log x dx.

thanks for any help,

Mitch
It would have helped if you showed the complete details of your working (your choice of u and dv etc.) because what little working you've posted is completely wrong.

See here: integrate x Log&#x5b;x&#x5d; - Wolfram|Alpha (click on Show steps).

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