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.
I get that, but what happens to the x in the denominator.
- 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.
- alexLv 76 years ago
u = ln(x)
---> integral of u^2 du = (u^3)/3 + C = (lnx)^3/3+C