\(\int \frac{e^{\sqrt{x}}\cos e^{\sqrt{x}}}{\sqrt{x}}dx\) is equal to
Answer & explanation
Correct answer: option 3
Let \(e^{\sqrt{x}}=t\) then \(dx=\frac{2\sqrt{x}}{e^{\sqrt{x}}}dt\)
\(\begin{aligned}\int \frac{e^{\sqrt{x}}\cos e^{\sqrt{x}}}{\sqrt{x}}dx&=2\int \cos tdt\\ &=2\sin e^{\sqrt{x}}+c\end{aligned}\)