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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals2 Marks
Question
Integrate the function $\frac{4 x+1}{\sqrt{2 x^{2}+x-3}}$
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Answer

The given Integrand is:
Let $2x^2 + x – 3 =t$
$\Rightarrow (4x + 1) dx = dt$
$\Rightarrow \int \frac{4 x+1}{\sqrt{2 x^{2}+x-3}} d x=\int \frac{1}{\sqrt{t}} d t$
$=2 \sqrt{t}+c$
$= 2 \sqrt{2 x^{2}+x-3}+C$

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