The integrals below involve `sqrt(ax+b)`.
1) `int 1/(sqrt(ax+b)) dx=(2sqrt(ax+b))/a`
2) `int x/sqrt(ax+b) dx=(2(ax-2b))/(3a^2)sqrt(ax+b)`
3) `int x^2/sqrt(ax+b) dx=(2(3a^2x^2-4abx+8b^2))/(15a^3)sqrt(ax+b)`
4) `int 1/(xsqrt(ax+b)) dx=1/sqrtbln((sqrt(ax+b)-sqrtb)/(sqrt(ax+b)+sqrtb))`
or: `=2/sqrt(-b)tan^-1sqrt((ax+b)/(-b))`
5) `int 1/(x^2sqrt(ax+b)) dx=-sqrt(ax+b)/(bx)-a/(2b) int 1/(xsqrt(ax+b)) dx` , See (4)
6) `int sqrt(ax+b) dx=(2sqrt((ax+b)^3))/(3a)`
7) `int xsqrt(ax+b) dx=(2(3ax-2b))/(15a^2)sqrt((ax+b)^3)`
8) `int x^2sqrt(ax+b) dx=(2(15a^2x^2-12abx+8b^2))/(105a^3)sqrt((ax+b)^3)`
9) `int sqrt(ax+b)/x dx=2sqrt(ax+b)+b int 1/(xsqrt(ax+b)) dx` , See (4)
10) `int sqrt(ax+b)/(x^2) dx=-sqrt(ax+b)/x+a/2 int 1/(xsqrt(ax+b)) dx` , See (4)
11) `int x^m/sqrt(ax+b) dx=(2x^msqrt(ax+b))/((2m+1)a)-(2mb)/((2m+1)a) int x^(m-1)/sqrt(ax+b) dx`
12) `int 1/(x^msqrt(ax+b)) dx=-sqrt(ax+b)/((m-1)bx^(m-1))-((2m-3)a)/((2m-2)b) int 1/(x^(m-1)sqrt(ax+b)) dx`
13) `int x^msqrt(ax+b) dx=(2x^m)/((2m+3)a)(ax+b)^(3/2)-(2mb)/((2m+3)a) int x^(m-1)sqrt(ax+b) dx`
14) `int sqrt(ax+b)/(x^m) dx=-sqrt(ax+b)/((m-1)x^(m-1))+a/(2(m-1)) int 1/(x^(m-1)sqrt(ax+b)) dx`
or: `=-(ax+b)^(3/2)/((m-1)bx^(m-1))-((2m-5)a)/((2m-2)b) int sqrt(ax+b)/x^(m-1) dx`
15) `int (ax+b)^(m/2) dx=(2(ax+b)^((m+2)/2))/(a(m+2))`
16) `int x(ax+b)^(m/2) dx=(2(ax+b)^((m+4)/2))/(a^2(m+4))-(2b(ax+b)^((m+2)/2))/(a^2(m+2))`
17) `int x^2(ax+b)^(m/2) dx=(2(ax+b)^((m+6)/2))/(a^3(m+6))-(4b(ax+b)^((m+4)/2))/(a^3(m+4))+(2b^2(ax+b)^((m+2)/2))/(a^3(m+2))`
18) `int ((ax+b)^(m/2))/x dx=(2(ax+b)^(m/2))/m+b int ((ax+b)^((m-2)/2))/x dx`
19) `int ((ax+b)^(m/2))/x^2 dx=-(ax+b)^((m+2)/2)/(bx)+(ma)/(2b) int (ax+b)^(m/2)/x dx`
20) `int 1/(x(ax+b)^(m/2)) dx=2/((m-2)b(ax+b)^((m-2)/2))+1/b int 1/(x(ax+b)^((m-2)/2)) dx`