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`