INTEGRALS CONTAINING ax+b AND px+q

nivedh_89

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3.: $displaystyle intdisplaystyle rac{dx}{(ax+b)^{displaystyle 2}(px+q)}=disp... ...laystyle rac{p}{bp-aq}lnleft(displaystyle rac{px+q}{ax+b} ight) ight}$
4.: $displaystyle intdisplaystyle rac{x,dx}{(ax+b)^{displaystyle2}(px+q)}=di... ...(displaystyle rac{ax+b}{px+q} ight)-displaystyle rac{b}{a(ax+b)} ight}$
5.: $displaystyleegin{array}{l} displaystyle intdisplaystyle rac{x^{display... ...displaystyle rac{b(bp-2aq)}{a^{displaystyle2}}ln(ax+b) ight} end{array}$
6.: $displaystyleegin{array}{l} displaystyle intdisplaystyle rac{dx}{(ax+b)^... ...rac{dx}{(ax+b)^{displaystyle m}(px+q)^{displaystyle n-1}} ight} end{array}$
7.: $displaystyle intdisplaystyle rac{ax+b}{px+q},dx=displaystyle rac{ax}{p}+displaystyle rac{bp-aq}{p^{displaystyle2}}ln(px+q)$
8.: $displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m}}{(px+q)^{displa... ...displaystyle m-1}}{(px+q)^{displaystyle n-1}},dx ight} end{array} ight.$