The integrals below involve `sqrt(x^2-a^2)`
1) `int 1/sqrt(x^2-a^2) dx = ln (x+sqrt(x^2-a^2))`
2) `int x/sqrt(x^2-a^2) dx = sqrt(x^2-a^2)`
3) `int x^2/sqrt(x^2-a^2) dx = (xsqrt(x^2-a^2))/2+a^2/2 ln (x+sqrt(x^2-a^2))`
4) `int x^3/sqrt(x^2-a^2) dx = (x^2-a^2)^(3/2)/3+a^2sqrt(x^2-a^2)`
5) `int 1/(xsqrt(x^2-a^2)) dx = 1/a sec^-1abs(x/a)`
6) `int 1/(x^2sqrt(x^2-a^2)) dx = sqrt(x^2-a^2)/(a^2x)`
7) `int 1/(x^3sqrt(x^2-a^2)) dx = sqrt(x^2-a^2)/(2a^2x^2)+1/(2a^3) sec^-1abs(x/a)`
8) `int sqrt(x^2-a^2) dx = (xsqrt(x^2-a^2))/2-a^2/2 ln (x+sqrt(x^2-a^2))`
9) `int xsqrt(x^2-a^2) dx = (x^2-a^2)^(3/2)/3`
10) `int x^2sqrt(x^2-a^2) dx = (x(x^2-a^2)^(3/2))/4+(a^2xsqrt(x^2-a^2))/8-a^4/8 ln (x+sqrt(x^2-a^2))`
11) `int x^3sqrt(x^2-a^2) dx = (x^2-a^2)^(5/2)/5+(a^2(x^2-a^2)^(3/2))/3`
12) `int sqrt(x^2-a^2)/x dx = sqrt (x^2-a^2)-a*sec^-1abs(x/a)`
13) `int sqrt(x^2-a^2)/x^2 dx = -sqrt (x^2-a^2)/x+ ln (x+sqrt(x^2-a^2))`
14) `int sqrt(x^2-a^2)/x^3 dx = -sqrt (x^2-a^2)/(2x^2)+1/(2a) sec^-1abs(x/a)`
15) `int 1/(x^2-a^2)^(3/2) dx = -x/(a^2sqrt(x^2-a^2))`
16) `int x/(x^2-a^2)^(3/2) dx = (-1)/sqrt(x^2-a^2)`
17) `int x^2/(x^2-a^2)^(3/2) dx = -x/sqrt(x^2-a^2)+ ln (x+sqrt(x^2-a^2))`
18) `int x^3/(x^2-a^2)^(3/2) dx = sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2`
19) `int 1/(x(x^2-a^2)^(3/2)) dx = (-1)/(a^2sqrt(x^2-a^2))-1/a^3 sec^-1 abs(x/a)`
20) `int 1/(x^2(x^2-a^2)^(3/2)) dx = -sqrt(x^2-a^2)/(a^4x)-x/(a^4sqrt(x^2-a^2)`
21) `int 1/(x^3(x^2-a^2)^(3/2)) dx = 1/(2a^2x^2sqrt(x^2-a^2))-3/(2a^4sqrt(x^2-a^2))-3/(2a^5) sec^-1 abs(x/a)`
22) `int (x^2-a^2)^(3/2) dx = (x(x^2-a^2)^(3/2))/4-(3a^2xsqrt(x^2-a^2))/8+3/8a^4 ln (x+sqrt(x^2-a^2))`
23) `int x(x^2-a^2)^(3/2) dx = (x^2-a^2)^(5/2)/5`
24) `int x^2(x^2-a^2)^(3/2) dx = (x(x^2-a^2)^(5/2))/6+(a^2x(x^2-a^2)^(3/2))/24-(a^4xsqrt(x^2-a^2))/16+a^6/16 ln (x+sqrt(x^2-a^2))`
25) `int x^3(x^2-a^2)^(3/2) dx = (x^2-a^2)^(7/2)/7+(a^2(x^2-a^2)^(5/2))/5`
26) `int (x^2-a^2)^(3/2)/x dx = (x^2-a^2)^(3/2)/3-a^2sqrt(x^2-a^2)+a^3 sec^-1abs(x/a)`
27) `int (x^2-a^2)^(3/2)/x^2 dx = -(x^2-a^2)^(3/2)/x+(3xsqrt(x^2-a^2))/2-3/2a^2 ln (x+sqrt(x^2-a^2))`
28) `int (x^2-a^2)^(3/2)/x^3 dx = -(x^2-a^2)^(3/2)/(2x^2)+(3sqrt(x^2-a^2))/2-3/2a*sec^-1 abs(x/a)`