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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 2 · Q28
Find: ∫ (2 x+3)/(x^2(x+3)) d x
Find : $\displaystyle \int \frac{2 x+3}{x^{2}(x+3)} d x$
Marking-scheme solution
$$\begin{aligned}
& I=\int \frac{2 x+3}{x^{2}(x+3)} d x=\int \frac{x+3}{x^{2}(x+3)} d x+\int \frac{x}{x^{2}(x+3)} d x \\
& I=\int \frac{1}{x^{2}} d x+\frac{1}{3} \int \frac{x+3-x}{x(x+3)} d x=\int \frac{1}{x^{2}} d x+\frac{1}{3} \int \frac{1}{x} d x-\frac{1}{3} \int \frac{1}{x+3} d x \\
& I=\frac{-1}{x}+\frac{1}{3} \log |x|-\frac{1}{3} \log |x+3|+c
\end{aligned}
$$
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.