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Question: Answered & Verified by Expert
$\int \frac{1+\tan x}{x+\log \sec x} d x=$
MathematicsIndefinite IntegrationJEE Main
Options:
  • A $\log (x+\log \sec x)+c$
  • B $-\log (x+\log \sec x)+c$
  • C $\log (x-\log \sec x)+c$
  • D None of these
Solution:
1412 Upvotes Verified Answer
The correct answer is: $\log (x+\log \sec x)+c$
Put $t=x+\log \sec x \Rightarrow d t=(1+\tan x) d x$, then
$\begin{aligned}
\int \frac{1+\tan x}{x+\log \sec x} d x & =\int \frac{1}{t} d t=\log t+c \\
& =\log (x+\log \sec x)+c
\end{aligned}$

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