Calc1.69

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\int {\frac  {x}{{\sqrt  {4+x^{2}}}}}\,dx\,

u=4+x^{2}\,

du=2x\,dx\,

\int {\frac  {x}{{\sqrt  {4+x^{2}}}}}\,dx={\frac  {1}{2}}\int {\frac  {du}{{\sqrt  {u}}}}=u^{{{\frac  {1}{2}}}}+C={\sqrt  {x^{2}+4}}+C\,

Click here to see this problem done by trigonometric substitution.


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