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Question Number 169677 by cortano1 last updated on 06/May/22

$$M=\int \frac{dx}{(x-4)\sqrt{x^2-6x+8}}=?$$

Answered by MJS_new last updated on 06/May/22

$$\int \frac{dx}{(x+c)\sqrt{x^2+ax+b}}=$$$$[t=\sqrt{x^2+ax+b}+x+\frac{a}{2}\to dx=\frac{\sqrt{x^2+ax+b}}{t}dt]$$$$=2\int \frac{dt}{t^2+(2c-a)t+\frac{a^2}{4}-b}$$$$\mathrm{here}a=-6\wedge b=8\wedge c=-4$$$$\Rightarrow$$$$M=2\int \frac{dt}{{(t^2-1)}^2}=-\frac{2}{t-1}=-\frac{2}{x-4+\sqrt{x^2-6x+8}}+C$$

Answered by cortano1 last updated on 06/May/22

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