CBSE 2026 · Region 2 · Set 2 · Q30 · 3 marks
Find : $\displaystyle \int \frac{2 x+1}{\sqrt{6 x+x^{2}}} \mathrm{~d} x$
Marking-scheme solution
$\displaystyle I=\int \dfrac{2x+1}{\sqrt{6x+x^{2}}}\, dx$
Let $\displaystyle 2x+1=A(6+2x)+B$
$\displaystyle \Rightarrow A=1, B=-5$
$\displaystyle \therefore I=\int \dfrac{6+2x}{\sqrt{6x+x^{2}}}\, dx-5 \int \dfrac{1}{\sqrt{6x+x^{2}}}\, dx$
$\displaystyle =2\sqrt{6x+x^{2}}-5 \int \dfrac{1}{\sqrt{(x+3)^{2}-3^{2}}}\, dx$
$\displaystyle =2\sqrt{6x+x^{2}}-5 \log\left|(x+3)+\sqrt{6x+x^{2}}\right|+C$
IntegralsMethods of IntegrationApplyshort_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.