INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b

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INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b

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2.: $displaystyle intdisplaystyle rac{x,dx}{displaystyle sqrt{ax+b}}=displaystyle rac{2(ax-2b)}{3a^{displaystyle2}}displaystyle sqrt{ax+b}$
3.: $displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{displaystyle sq... ...le2}-4abx+8b^{displaystyle 2})}{15a^{displaystyle3}}displaystyle sqrt{ax+b}$
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5.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle 2}displaystyle sqr... ...rac{a}{2b}displaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}$
6.: $displaystyle intdisplaystyle sqrt{ax+b},dx=displaystyle rac{2displaystyle sqrt{(ax+b)^{displaystyle3}}}{3a}$
7.: $displaystyle int xdisplaystyle sqrt{ax+b},dx=displaystyle rac{2(3ax-2b)}{15a^{displaystyle2}}displaystyle sqrt{(ax+b)^{displaystyle3}}$
8.: $displaystyle int x^{displaystyle2}displaystyle sqrt{ax+b},dx=displaystyl... ...aystyle 2})}{105a^{displaystyle3}}displaystyle sqrt{(a+bx)^{displaystyle3}}$
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10.: $displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...frac{a}{2}displaystyle intdisplaystyle rac{dx}{xdisplaystyle sqrt{ax+b}}$
11.: $displaystyle intdisplaystyle rac{x^{displaystyle m}}{displaystyle sqrt{... ...e intdisplaystyle rac{x^{displaystyle m-1}}{displaystyle sqrt{ax+b}},dx$
12.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle m}displaystyle sqr... ...yle intdisplaystyle rac{dx}{x^{displaystyle m-1}displaystyle sqrt{ax+b}}$
13.: $displaystyle int x^{displaystyle m}displaystyle sqrt{ax+b},dx=displaysty... ...}{(2m+3)a}displaystyle int x^{displaystyle m-1}displaystyle sqrt{ax+b},dx$
14.: $displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...yle intdisplaystyle rac{dx}{x^{displaystyle m-1}displaystyle sqrt{ax+b}}$
15.: $displaystyle intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaysty... ...e intdisplaystyle rac{displaystyle sqrt{ax+b}}{x^{displaystyle m-1}},dx$
16.: $displaystyle int(ax+b)^{displaystyle m/2},dx=displaystyle rac{2(ax+b)^{displaystyle(m+2)/2}}{a(m+2)}$
17.: $displaystyle int x(ax+b)^{displaystyle m/2},dx=displaystyle rac{2(ax+b)^... ...}-displaystyle rac{2b(ax+b)^{displaystyle(m+2)/2}}{a^{displaystyle2}(m+2)}$
18.: $egin{array}{lcl} displaystyle int x^{displaystyle2}(ax+b)^{displaystyle m... ...splaystyle2}(ax+b)^{displaystyle(m+2)/2}}{a^{displaystyle3}(m+2)} end{array}$
19.: $displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x},dx=displ... ...m}+bdisplaystyle intdisplaystyle rac{(ax+b)^{displaystyle(m-2)/2}}{x},dx$
20.: $displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x^{displayst... ...ma}{2b}displaystyle intdisplaystyle rac{(ax+b)^{displaystyle m/2}}{x},dx$
21.: $displaystyle intdisplaystyle rac{dx}{x(ax+b)^{displaystyle m/2}}=display... ...{1}{b}displaystyle intdisplaystyle rac{dx}{x(ax+b)^{displaystyle(m-2)/2}}$

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INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b