Question

Please help to evaluate the integral:
∫x^2 ln (x^2)dx

Answer 1

you would have to use integration by parts.....

Answer 2

Thats what I thought lol

Answer 3

then your thoughts were right....i am sure you were doubting yourself..

Answer 4

I haven't done an integral since last august lol

Answer 5

Yes thanks, if I let u = x^2 then du = 2x dx and dv = ln (x^2), what would v = ?

Answer 6

The formula for integration by parts,

integral f(x)g'(x)dx = f(x)g(x) - integral f'(x)g(x)dx

Answer 7

hope this link helps. http://www.youtube.com/watch?v=dqaDSlYdRcs...

Answer 8

There is a really good video on khan academy but I cant seem to find it :(

Answer 9

http://www.youtube.com/watch?v=g-Uxw0eKuJo
is that it??

Answer 10

Maybe,

Anyways,

Take your integral and split it into two functions ∫x^2 ln (x^2)dx

for example

set,

f(x) = x^2
g'(x) = ln(x^2)

then input them in the formula

f(x)g(x) - integral f'(x)g(x)dx

You should try to do this in a way so that you get the simplest integral possible


I hope this explanation is helpful but you may want to check out the posted videos it is easier when someone explains it to you

Answer 11

Thanks Australopithecus and kausarsalley - I understand the formula, but am struggling with the bit where I need to find the integral of ln (x^2). Appreciate your help!

Answer 12

or does solves a problem with it rather

Answer 13

REMEMBER LOG RULES!
ln(x^2) = 2ln(x)

Answer 14

I suspect you can solve it now ;)

Answer 15

You should have a table that tells you the derivative of ln(x)

Answer 16

oh sorry lol, been awhile since i have done an integral, I'm pretty sure that is something you are suppose to memorize

Answer 17

you can just use u substitution I'm pretty sure though

Answer 18

set u = ln(x)

Answer 19

Yes I need to memorize it indeed! derivative of ln(x) is 1/x, but would integral of 2lnx then be 2xlnx - 2x? I think I'll try u = ln(x^2) yes thanks!

Answer 20

looks good to me

Answer 21

Thanks for your help - I ended up using u = ln(x^2) then du = 2/x dx and dv = x^2 then v = x^3/3 and using the formula managed to get the answer.