# Integral of ln Squared?

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• May 1st 2010, 01:57 PM
iPod
Integral of ln Squared?
$\int\ln^2(x)dx$

Hints please? (Crying)
• May 1st 2010, 02:11 PM
TKHunny
Looks like a prime candidate for "Parts". It's almost an eyeball problem.

$x\cdot ln^{2}(x) - \int x\cdot 2\cdot ln(x)\cdot \frac{1}{x}\;dx$
• May 1st 2010, 02:15 PM
iPod
soo,

$\ln^2(x)-2x\ln(x)+2x+C$

??
• May 1st 2010, 02:22 PM
pickslides
close, try $x\ln^2(x)-2x\ln(x)+2x+C$
• May 1st 2010, 02:22 PM
TKHunny
So close! Give it another go. This time, don't lose the 'x' on the front.
• May 1st 2010, 02:23 PM
harish21
Quote:

Originally Posted by iPod
soo,

$\ln^2(x)-2x\ln(x)+2x+C$

??

You should get
$x\ln^2(x)-2x\ln(x)+2x+C$
• May 1st 2010, 02:26 PM
iPod
woopsy, that was a typo ^^

i meant to right
$x\ln^2(x)-2x\ln(x)+2x+C$

but I have seen what you have done tkhunny, using the 'by parts rule, you have integrated it as if it was

$\int1.\ln^2(x)$

right?
• May 1st 2010, 02:30 PM
pickslides
Quote:

Originally Posted by iPod

$\int1.\ln^2(x)$

right?

Yep with $v = \ln^2x$ and $du = 1$
• May 1st 2010, 02:35 PM
iPod
Thanks you lot :D
• May 1st 2010, 04:12 PM
TKHunny
...except that I don't use that silly American method. The Russians are much more visual and literal.