The integrals below involve √ax+b and px+q occurring together in the integrand.
1) ∫px+q√ax+b dx=2(apx+3aq-2bp)3a2√ax+b
2) ∫1(px+q)√ax+b dx=1√bp-aq√pln(√p(ax+b)-√bp-aq√p(ax+b)+√bp-aq)
OR =2√aq-bp√ptan-1√p(ax+b)aq-bp
3) ∫√ax+bpx+q dx=2√ax+bp+√bp-aqp√qln(√p(ax+b)-√bp-aq√p(ax+b)+√bp-aq)
OR =2√ax+bp-2√aq-bpp√ptan-1√p(ax+b)aq-bp
4) ∫(px+q)n√ax+b dx=2(px+q)n+1√ax+b(2n+3)p+bp-aq(2n+3)p∫(px+q)n√ax+bdx
5) ∫1(px+q)n√ax+b dx=√ax+b(n-1)(aq-bp)(px+q)n-1+(2n-3)a2(n-1)(aq-bp)∫1(px+q)n-1√ax+b dx
6) ∫(px+q)n√ax+b dx=2(px+q)n√ax+b(2n+1)a+2n(aq-bp)(2n+1)a∫(px+q)n-1√ax+b dx
7) ∫√ax+b(px+q)n dx=-√ax+b(n-1)p(px+q)n-1+a2(n-1)p∫1(px+q)n-1√ax+b dx