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Mathematics · 2025 · 5 marks
CBSE 2025 · Region 2 · Set 1 · Q33
Find: ∫ (x^2+x+1)/((x+2)(x^2+1)) d x.
Find : $\displaystyle \int \frac{x^{2}+x+1}{(x+2)\left(x^{2}+1\right)} \mathrm{d} x$.
Marking-scheme solution
\[\begin{aligned}
& \frac{x^{2}+x+1}{(x+2)\left(x^{2}+1\right)}=\frac{A}{(x+2)}+\frac{B x+c}{x^{2}+1} \\
& \text { Getting } A=\frac{3}{5}, B=\frac{2}{5}, C=\frac{1}{5} \\
& \text { Given integral }=\frac{3}{5} \int \frac{1}{x+2} \mathrm{d} x+\frac{1}{5} \int \frac{2 x}{x^{2}+1} \mathrm{d} x+\frac{1}{5} \int \frac{1}{x^{2}+1} \mathrm{d} x
\end{aligned}
\]
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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.