2x-3-dx-x-2-4x-7-

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

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

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

= \int \frac{2 x + 4 - 1}{\sqrt{x^{2} + 4 x - 7}} d x

= \int \frac{2 x + 4}{\sqrt{x^{2} + 4 x - 7}} d x - \int \frac{d x}{\sqrt{{(x + 2)}^{2} - {(\sqrt{11})}^{2}}}

= \int \frac{d t}{\sqrt{t}} - l n ∣ (x + 2) + \sqrt{{{(x + 2)}^{2} - \sqrt{(11})}^{2}} ∣, w h e r e t = x^{2} + 4 x - 7

= 2 \sqrt{t} - l n ∣ x + 2 + \sqrt{x^{2} + 4 x - 7} ∣ + C

= 2 \sqrt{x^{2} + 4 x - 7} - l n ∣ x + 2 + \sqrt{x^{2} + 4 x - 7} ∣ + C

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