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

Integrate : $\int \large\frac{1+\tan ^2 x }{1+\tan x }$$dx$

$(a)\;\log _e |\sec^2 x |+c \\(b)\;\sec^2 x +c \\(c)\;\log _e |\tan ^2 x |+c \\ (d)\;None$

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A)
$1+\tan x =t$
differentiate on both sides with respect to
$\sec^2 x dx =dt$
=>$\int \large\frac{dt}{t}$
$\log _e |\sec^2 x |+c$
Hence a is the correct answer.
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