# How do I get the integral of (ln(x))^2/x?

I know the answer is ln(x)^3/3 but dont know why it is.

Update:

I get that, but what happens to the x in the denominator.

### 2 Answers

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- HuhLv 66 years agoFavourite answer
∫ [((ln(x))^2 / x] dx

Perform a u-substitution with the natural logarithm: u = ln(x)

Thus the derivative of u: du = [1 / x] dx

∫ u^2 du

Perform power rule of integration: add one to the power and divide by the new power:

= u^3 / 3 + C

Undo the substitution:

= [ln(x)]^3 / 3 + C

... while C is the constant of integration.

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