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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 3 · Q27
Find: ∫ (3 x-1)/(√(x^2-4 x)) d x
Find : $\displaystyle \int \frac{3 x-1}{\sqrt{x^{2}-4 x}} \mathrm{~d} x$
Marking-scheme solution
$\displaystyle I=\int \dfrac{3x-1}{\sqrt{x^{2}-4x}}\, dx$
Put $\displaystyle 3x-1=A(2x-4)+B$
$\displaystyle \Rightarrow A=\dfrac{3}{2}, B=5$
$\displaystyle \therefore I=\dfrac{3}{2} \int \dfrac{2x-4}{\sqrt{x^{2}-4x}}\, dx+5 \int \dfrac{1}{\sqrt{x^{2}-4x}}\, dx$
$\displaystyle =3\sqrt{x^{2}-4x}+5 \int \dfrac{1}{\sqrt{(x-2)^{2}-2^{2}}}\, dx$
$\displaystyle =3\sqrt{x^{2}-4x}+5 \log\left|(x-2)+\sqrt{x^{2}-4x}\right|+C$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.