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Table of Integrals - Forms Involving ax+b and px+q

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

1) px+qax+b dx=2(apx+3aq-2bp)3a2ax+b

2) 1(px+q)ax+b dx=1bp-aqpln(p(ax+b)-bp-aqp(ax+b)+bp-aq)


                                OR =2aq-bpptan-1p(ax+b)aq-bp


3) ax+bpx+q dx=2ax+bp+bp-aqpqln(p(ax+b)-bp-aqp(ax+b)+bp-aq)


                    OR =2ax+bp-2aq-bppptan-1p(ax+b)aq-bp


4) (px+q)nax+b dx=2(px+q)n+1ax+b(2n+3)p+bp-aq(2n+3)p(px+q)nax+bdx


5) 1(px+q)nax+b dx=ax+b(n-1)(aq-bp)(px+q)n-1+(2n-3)a2(n-1)(aq-bp)1(px+q)n-1ax+b dx


6) (px+q)nax+b dx=2(px+q)nax+b(2n+1)a+2n(aq-bp)(2n+1)a(px+q)n-1ax+b dx


7) ax+b(px+q)n dx=-ax+b(n-1)p(px+q)n-1+a2(n-1)p1(px+q)n-1ax+b dx