Question

$\int \frac{k^{\sqrt{x}}}{\sqrt{x}}dx=$

• A. $k^{\sqrt{x}}\log e^k+c$
• B. $\frac{2k^{\sqrt{x}}}{lnk}+c$
  
• C. $2k^{\sqrt{x}}\log {10}^k+c$
• D. $2k^{\sqrt{x}}/\log e^k+c$

Answer 1

The correct option is B $\frac{2k^{\sqrt{x}}}{lnk}+c$

$I=\int \frac{k^{\sqrt{x}}}{\sqrt{x}}dxput\sqrt{x}=t\frac{1}{2\sqrt{x}}dx=dtI=2\int k^{t}dt=2\left(\frac{k^t}{lnk}\right)+c=\frac{2k^{\sqrt{x}}}{lnk}+c$