Question

$\int \frac{1}{\log a}\left(a^{x} \cos a^{x}\right) d x=$

• A. $\frac{1}{(\log a)^{2}} \sin a^{x}+C$
• B. $(\log a)^{2} \sin a^{x}+C$
• C. $\frac{1}{\log a} \sin a^{x}+C$
• D. $\sin a^{x}+C$
• E. $a^{x} \sin a^{x}+C$

Answer 1

Answer: (A)

Put $a^{x}=v \Rightarrow a^{x} d x=\frac{d v}{\log a^{'}}$ then it reduces to
$\int \frac{ l }{(\log a)^{2}} \cos \,v \,d v=\frac{ l }{(\log a)^{2}} \sin\, v+C$
$=\frac{1}{(\log a)^{2}} \sin a^{x}+C$