Integral Calculus Question 223
Question: $ \int_{{}}^{{}}{\frac{1}{\log a}(a^{x}\cos a^{x})dx=} $
Options:
A) $ \sin a^{x}+c $
B) $ a^{x}\sin a^{x}+c $
C) $ \frac{1}{{{(\log a)}^{2}}}\sin a^{x}+c $
D) $ \log \sin a^{x}+c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{\frac{1}{\log a}(a^{x}\cos a^{x}),dx} $ Put $ a^{x}=t\Rightarrow a^{x}dx=\frac{dt}{\log a}, $ then it reduces to $ \int_{{}}^{{}}{\frac{1}{{{(\log a)}^{2}}}\cos t,dt}=\frac{1}{{{(\log a)}^{2}}}\sin t+c=\frac{1}{{{(\log a)}^{2}}}\sin a^{x}+c $ .
BETA
