# Table of Integrals - Forms Involving ln x

The integrals below involve ln x

1) int  ln x dx = x lnx-x

2) int  x lnx  dx = x^2/2(ln x-1/2)

3) int  x^m lnx  dx = x^(m+1)/(m+1)(ln x-1/(m+1))

**[If m=-1, see integral #4 in this table]

4) int  ln x/x  dx = 1/2 ln^2x

5) int  ln x/x^2  dx = -ln x/x-1/x

6) int  ln^2x  dx = x ln^2x-2x ln x+2x

7) int  ln^nx/x  dx = (ln^(n+1)x)/(n+1)

**[If n=-1, see integral #8 in this table]

8) int  1/(x lnx)  dx = ln(lnx)

9) int  1/ln x  dx = ln(ln x)+ln x+ln^2x/(2*2!)+ln^3x/(3*3!)+...

10) int  x^m/ln x  dx = ln(ln x)+(m+1)ln x+((m+1)^2ln^2x)/(2*2!)+((m+1)^3ln^3 x)/(3*3!)+...

11) int  ln^nx  dx = x*ln^n x-nint  ln^(n-1)x  dx

12) int  x^m ln^n x  dx = (x^(m+1)ln^n x)/(m+1)-n/(m+1)int  x^m ln^(n-1) x  dx

**[If m=-1, see integral #7 in this table]

13) int  ln(x^2+a^2)  dx = x*ln(x^2+a^2)-2x+2a*tan^-1(x/a)

14) int  ln(x^2-a^2)  dx = x*ln(x^2-a^2)-2x+a*ln((x+a)/(x-a))

15) int  x^m ln(x^2+-a^2)  dx = (x^(m+1)ln(x^2+-a^2))/(m+1)-2/(m+1)int  x^(m+2)/(x^2+-a^2)  dx