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Question Number 20256 by tammi last updated on 24/Aug/17

$$\int \frac{dx}{(x-4)\sqrt{x+3}}$$

Answered by Tinkutara last updated on 24/Aug/17

$$x+3=t^2$$$$dx=2tdt$$$$x-4=t^2-7$$$$\int \frac{dx}{(x-4)\sqrt{x+3}}=\int \frac{2tdt}{(t^2-7)t}=2\int \frac{dt}{t^2-7}$$$$=2\left(\frac{1}{2\sqrt{7}}\right)\log \mid \frac{t-\sqrt{7}}{t+\sqrt{7}}\mid +C$$$$=\frac{1}{\sqrt{7}}\log \mid \frac{\sqrt{x+3}-\sqrt{7}}{\sqrt{x+3}+\sqrt{7}}\mid +C$$

Commented by tammi last updated on 25/Aug/17

$$thanks$$

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