Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evalute : $\int \frac{2 x+6}{\sqrt{x^2+6 x+3}} d x$
✓
Answer
$ \text { Let } I=\int \frac{2 x+6}{\sqrt{x^2+6 x+3}} d x $ Put $x^2+6 x+3=t$ $ \begin{aligned} & \therefore(2 x+6) d x=d t \\ & \therefore I=\int \frac{1}{\sqrt{t}} d t=\int t^{-\frac{1}{2}} d t \end{aligned} $ $ =\frac{t^{\frac{1}{2}}}{1 / 2}+c=2 \sqrt{x^2+6 x+3}+c . $
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