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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS4 Marks
Question
Evaluate: $\int\frac{\text{5x + 3}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}$.
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Answer

$\text{I}=\int\frac{\text{5x + 3}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}\text{dx}=\int\frac{\frac{5}{2}\text{(2x + 4)}-7}{\sqrt{\text{x}^{2}+\text{4x}+10}}$

$=\frac{5}{2} \int\frac{\text{2x + 4}}{\sqrt{\text{x}^{2}+\text{4x + 10}}}\text{dx}-7 \int\frac{1}{\sqrt{\text{(x+2)}^{2}+(\sqrt{6})^{2}}}\text{dx}$

$ =5\cdot\sqrt{\text{x}^{2}+\text{4x + 10}}-7\log|\text{(x + 2)}+\sqrt{\text{x}^{2}+\text{4x}+10}|+\text{c}$.

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