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

Integrate : $ \int x \sec ^2x^2 .dx$

\[\begin {array} {1 1} (a)\;\frac{1}{2} \sec(x^2)+c \\ (b)\;\frac{1}{2} \tan(x^2)+c \\ (c)\;\frac{1}{2} \sec(x^2)+c \\ (d)\;None \end {array}\]

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A)
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$x^2=t$
$2xdx=dt$
$\int \large\frac{1}{2} . $$\sec^2 t. dt $
$ \large\frac{1}{2} $$ \int \sec^2 t. dt $
$ \large\frac{1}{2} $$ \tan t+c $
$ \large\frac{1}{2} $$ \tan (x^2)+c $
Hence b is the correct answer.
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