# Table of Integrals - Forms Involving sqrt(ax+b) and px+q

The integrals below involve sqrt(ax+b) and px+q occurring together in the integrand.

1) int (px+q)/sqrt(ax+b)  dx = (2(apx+3aq-2bp))/(3a^2) sqrt(ax+b)

2) int 1/((px+q)sqrt(ax+b))  dx = 1/(sqrt(bp-aq)sqrtp) ln ((sqrt(p(ax+b))-sqrt(bp-aq))/(sqrt(p(ax+b))+sqrt(bp-aq)))

OR = 2/(sqrt(aq-bp)sqrtp) tan^-1 sqrt((p(ax+b))/(aq-bp))

3) int sqrt(ax+b)/(px+q)  dx = (2sqrt(ax+b))/p+sqrt(bp-aq)/(psqrtq) ln ((sqrt(p(ax+b))-sqrt(bp-aq))/(sqrt(p(ax+b))+sqrt(bp-aq)))

OR = (2sqrt(ax+b))/p-(2sqrt(aq-bp))/(psqrtp) tan^-1 sqrt((p(ax+b))/(aq-bp))

4) int (px+q)^nsqrt(ax+b)  dx = (2(px+q)^(n+1)sqrt(ax+b))/((2n+3)p)+(bp-aq)/((2n+3)p) int (px+q)^n/sqrt(ax+b) dx

5) int 1/((px+q)^nsqrt(ax+b))  dx = (sqrt(ax+b))/((n-1)(aq-bp)(px+q)^(n-1))+((2n-3)a)/(2(n-1)(aq-bp)) int 1/((px+q)^(n-1)sqrt(ax+b))  dx

6) int (px+q)^n/sqrt(ax+b)  dx = (2(px+q)^nsqrt(ax+b))/((2n+1)a)+(2n(aq-bp))/((2n+1)a) int (px+q)^(n-1)/sqrt(ax+b)  dx

7) int sqrt(ax+b)/(px+q)^n  dx = (-sqrt(ax+b))/((n-1)p(px+q)^(n-1))+a/(2(n-1)p) int 1/((px+q)^(n-1)sqrt(ax+b))  dx