Question

Integrate dx/(4+2²)½ dx

Answer 1

∫$\frac{x}{(4+2^2)^{1/2}}dx$  

$=\frac{1}{(4+2^2)^{1/2}} \int xdx$

$=\frac{x^2}{2} \cdot \frac{1}{(4+2^2)^{1/2}}+C$

$=\frac{x^2}{2}\cdot \frac{1}{2 \cdot 2^{1/2}}+C$

$=\frac{x^2}{4 \cdot 2^{1/2}}+C$

Answer: $\frac{x^2}{4 \cdot 2^{1/2}}+C$