CUET Preparation Today
| \(\int \frac{e^{\sqrt{x}}\cos e^{\sqrt{x}}}{\sqrt{x}}dx\) is equal to |
\(\sin (e^{\sqrt{x}})+c\) \(\cos (e^{\sqrt{x}})+c\) \(2\sin (e^{\sqrt{x}})+c\) None of these |
| \(2\sin (e^{\sqrt{x}})+c\) |
| Let \(e^{\sqrt{x}}=t\) then \(dx=\frac{2\sqrt{x}}{e^{\sqrt{x}}}dt\) \(\begin{aligned}\int \frac{e^{\sqrt{x}}\cos e^{\sqrt{x}}}{\sqrt{x}}dx&=2\int \cos tdt\\ &=2\sin e^{\sqrt{x}}+c\end{aligned}\) |
