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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration by Substitution

  • question_answer
    \[\int{x{{e}^{{{x}^{2}}}}}dx=\]                                  [RPET 2003]

    A)            \[-\frac{{{e}^{{{x}^{2}}}}}{2}+c\]

    B)            \[\frac{{{e}^{{{x}^{2}}}}}{2}+c\]

    C)            \[\frac{{{e}^{x}}}{2}+c\]

    D)  \[-\frac{{{e}^{x}}}{2}+c\]

    Correct Answer: B

    Solution :

                       \[I=\int{x{{e}^{{{x}^{2}}}}dx}\]\[=\frac{1}{2}\int{{{e}^{t}}dt=\frac{{{e}^{{{x}^{2}}}}}{2}}+c\].                                                                       {Put \[{{x}^{2}}=t\] Þ \[2xdx=dt\]}


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