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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{5}{8}.x.e{^{\Large x^2}}. \sec (e^{\Large x^2}).\tan (e^{x^2})dx$

$(a)\;\frac{5}{6} \sin (e^{x^2})+c \\(b)\;\sec (e^{x^2})+\tan (e^{x^2})+c \\(c)\;\frac{5}{16} \sec (e^{x^2})+c \\ (d)\;\frac{5}{16} \tan (e^{x^2})+c $

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A)
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$e^{x^2}=t$
$2.e^{x^2}dx=dt$
=>$\large\frac{1}{2} $$ \int \frac{5}{8} . \sec t. \tan t ,dt$
=> $\large\frac{5}{16} $$ \int \sec t \tan t .dt$
=> $\large\frac{5}{16}$$ \times \sec t +c$
$\large\frac{5}{16}$$ \sec (e^{x^2})+c$
Hence c is the correct answer.
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