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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 2 · Set 3 · Q22
Find: ∫ 2 x^3 e^x^2 d x.
Find: $\displaystyle \int 2 x^{3} \mathrm{e}^{x^{2}} \mathrm{~d} x$.
Marking-scheme solution
\[\begin{aligned}
& I=\int 2 x^{3} \mathrm{e}^{x^{2}} d x=\int 2 x x^{2} \mathrm{e}^{x^{2}} d x \\
& \text { Put } x^{2}=t \Rightarrow 2 x d x=d t \\
& I=\int t \mathrm{e}^{t} d t \\
& =t \mathrm{e}^{t}-\int \mathrm{e}^{t} d t \\
& =t \mathrm{e}^{t}-\mathrm{e}^{t}+C \\
& =\mathrm{e}^{x^{2}}\left(x^{2}-1\right)+C
\end{aligned}
\]
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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.