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Question Number 20239 by tammi last updated on 24/Aug/17

$$\int \frac{(2x+3)dx}{\sqrt{x^2+4x-7}}$$

Answered by $@ty@m last updated on 25/Aug/17

$$=\int \frac{2x+4-1}{\sqrt{x^2+4x-7}}dx$$$$=\int \frac{2x+4}{\sqrt{x^2+4x-7}}dx-\int \frac{dx}{\sqrt{{(x+2)}^2-{\left(\sqrt{11}\right)}^2}}$$$$=\int \frac{dt}{\sqrt{t}}-ln\mid (x+2)+\sqrt{{{(x+2)}^2-\sqrt{(11})}^2}\mid ,wheret=x^2+4x-7$$$$=2\sqrt{t}-ln\mid x+2+\sqrt{x^2+4x-7}\mid +C$$$$=2\sqrt{x^2+4x-7}-ln\mid x+2+\sqrt{x^2+4x-7}\mid +C$$

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