# Thread: Integral of ln Squared?

1. ## Integral of ln Squared?

$\displaystyle \int\ln^2(x)dx$

2. Looks like a prime candidate for "Parts". It's almost an eyeball problem.

$\displaystyle x\cdot ln^{2}(x) - \int x\cdot 2\cdot ln(x)\cdot \frac{1}{x}\;dx$

3. soo,

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

??

4. close, try $\displaystyle x\ln^2(x)-2x\ln(x)+2x+C$

5. So close! Give it another go. This time, don't lose the 'x' on the front.

6. Originally Posted by iPod
soo,

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

??
You should get
$\displaystyle x\ln^2(x)-2x\ln(x)+2x+C$

7. woopsy, that was a typo ^^

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

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

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

right?

8. Originally Posted by iPod

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

right?
Yep with $\displaystyle v = \ln^2x$ and $\displaystyle du = 1$

9. Thanks you lot

10. ...except that I don't use that silly American method. The Russians are much more visual and literal.