CUET Preparation Today
| The value of \(\int \frac{a^{\sqrt{x}}}{\sqrt{x}}dx\) is |
\(a^{\sqrt{x}} \log_{e} a+c\) \(2a^{\sqrt{x}} \log_{e} a+c\) \(2a^{\sqrt{x}} \log_{10} e+c\) \(2a^{\sqrt{x}} \log_{a} e+c\) |
| \(2a^{\sqrt{x}} \log_{a} e+c\) |
| Let \(\sqrt{x}=t\) so \(dx=2\sqrt{x} dt\) \(\begin{aligned}\int \frac{a^{\sqrt{x}}{\sqrt{x}}dx&=2\int a^{t}dt \\ &=\frac{2a^{t}}{\log_{e} a}+c\end{aligned}\) |
