Tangent Substitution Formulas

`TanSub 1.  `*Int((a^2+u^2)^(1/2),u) = 1/2*u*(a^2+u^2)^(1/2)+1/2*a^2*ln(u+(a^2+u^2)^(1/2))

`TanSub 2.  `*Int(u^2*(a^2+u^2)^(1/2),u) = 1/8*u*(a^2+2*u^2)*(a^2+u^2)^(1/2)-1/8*a^4*ln(u+(a^2+u^2)^(1/2))

`TanSub 3.  `*Int((a^2+u^2)^(1/2)/u,u) = (a^2+u^2)^(1/2)-a*ln(abs((a+(a^2+u^2)^(1/2))/u))

`TanSub 4.  `*Int((a^2+u^2)^(1/2)/u^2,u) = -(a^2+u^2)^(1/2)/u+ln(u+(a^2+u^2)^(1/2))

`TanSub 5.  `*Int(1/((a^2+u^2)^(1/2)),u) = ln(u+(a^2+u^2)^(1/2))

`TanSub 6.  `*Int(u^2/(a^2+u^2)^(1/2),u) = 1/2*u*(a^2+u^2)^(1/2)-1/2*a^2*ln(u+(a^2+u^2)^(1/2))

`TanSub 7.  `*Int(1/((a^2+u^2)^(1/2)*u),u) = -1/a*ln(abs((a+(a^2+u^2)^(1/2))/u))

`TanSub 8.  `*Int(1/(u^2*(a^2+u^2)^(1/2)),u) = -1/u*(a^2+u^2)^(1/2)/a^2

`TanSub 9.  `*Int(1/((a^2+u^2)^(3/2)),u) = 1/(a^2+u^2)^(1/2)/a^2*u

`TanSub 10.  `*Int(u^2/(a^2+u^2)^(3/2),u) = -1/(a^2+u^2)^(1/2)*u+ln(u+(a^2+u^2)^(1/2))

`TanSub 11.  `*Int(u^2/(a^2+u^2)^(5/2),u) = 1/3/(a^2+u^2)^(3/2)/a^2*u^3