e ^ 2 ^ -1 x (1+ x )^ 2 (1+ x ^ 2 ) dx is equal to
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\[\int \frac{\mathrm{e}^{2 \tan ^{-1} x}(1+\mathrm{x})^{2}}{\left(1+\mathrm{x}^{2}\right)} \mathrm{dx} \text { is equal to }\]
- \(x e^{\tan ^{-1} x}+c\)
- \(\mathrm{xe}^{2 \tan ^{-1} \mathrm{x}}+\mathrm{c}\)
- \(2 x \mathrm{e}^{2 \tan ^{-1} \mathrm{x}}+\mathrm{c}\)
- none of these
Answer
(B) xe ^ 2 ^ -1 x + c
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