Integral Calculus Question 407
Question: $ \int_{{}}^{{}}{\frac{\tan (\log x)}{x}\ dx=} $
Options:
A) $ \log \cos (\log x)+c $
B) $ \log \sin (\log x)+c $
C) $ \log \sec (\log x)+c $
D) $ \log cosec(\log x)+c $
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Answer:
Correct Answer: C
Solution:
Put $ \log x=t\Rightarrow \frac{1}{x}dx=dt $ , therefore $ \int_{{}}^{{}}{\frac{\tan (\log x)}{x}dx=\int_{{}}^{{}}{\tan t\ dt}} $ $ =\log \sec t+c=\log \ \sec (\log x)+c $ .
BETA
