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Mathematics · 2025 · 5 marks
CBSE 2025 · Region 7 · Set 3 · Q32
(a) Find: ∫ (3 x+1)/((x-2)^2(x+2)) d x
(a)
Find : \[\int \frac{3 x+1}{(x-2)^{2}(x+2)} d x \]
OR
(b)
Evaluate : \[\int_{0}^{\pi / 2} \frac{x}{\cos x+\sin x} d x \]
Marking-scheme solution
(a)
Using Partial fractions,
\[\begin{aligned}
\int \frac{3 x+1}{(x-2)^{2}(x+2)} d x & =\frac{5}{16} \int \frac{1}{x-2} d x+\frac{7}{4} \int \frac{1}{(x-2)^{2}} d x-\frac{5}{16} \int \frac{1}{x+2} d x \\
& =\frac{5}{16} \log |x-2|-\frac{7}{4(x-2)}-\frac{5}{16} \log |x+2|+C \\
o r & =\frac{5}{16} \log \left|\frac{x-2}{x+2}\right|-\frac{7}{4(x-2)}+C
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.