Question

Evaluate: $\int \frac{e^{\sqrt{x}}\cos (e^{\sqrt{x})}}{\sqrt{x}}dx$

• A. $2\sin e^{\sqrt{x}}$
• B. $2\cos e^{\sqrt{x}}$
• C. $\sin e^{\sqrt{x}}$
• D. $\tan e^{\sqrt{x}}$

Answer 1

The correct option is A $2\sin e^{\sqrt{x}}$

Substitute $e^{\sqrt{x}}=t$

$\therefore e^{\sqrt{x}}.\frac{1}{2\sqrt{\left(x\right)}}dx=dt.$

$I=2\int \cos tdt=2\sin t+c=2\sin e^{\sqrt{x}}+c.$