Mathematics

Evaluate
$$\int { x-3 } \sqrt { { x }^{ 2 }+4x+3 } dx$$


SOLUTION
$$\displaystyle\int \sqrt{x^{2}+4{x}+3}dx=\displaystyle\int \sqrt{(x+2)^{2}-1}\ dx=\dfrac{(x+2)}{2}\sqrt{(x+2)^{2}-1}-\dfrac{1}{2}\ln \mid (x+2)+\sqrt{(x+2)^{2}-1}\ \mid $$
$$\displaystyle\int (x-3\sqrt{x^{2}+4{x}+3})dx=\ \dfrac{x^{2}}{2}-\dfrac{3}{2}(x+2)\sqrt{x^{2}+4{x}+3}+\dfrac{3}{2}\ln \mid x+2+\sqrt{x^{2}+4{x}+3} \ \mid+C$$
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Subjective Medium Published on 17th 09, 2020
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