Integration Question

[ciluvmathf]

i have been trying to work this out for a while how. How would i go about doing this?

 

[MarkFL]

I would use the suggested substitution:

[MATH]u=x^2+4\implies du=2x\,dx[/MATH]
And then write:

[MATH]I=\frac{1}{2}\int \sqrt{x^2+4}\,2x\,dx=\frac{1}{2}\int u^{\frac{1}{2}}\,du[/MATH]
Can you proceed?