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