integrate (4) / (4(x^1/2) + 4)
please help me i cannot seem to get this
i believe i need a u substitution, but i am not sure
thanks in advance
$\displaystyle
\begin{gathered}
\int {\frac{4}
{{4\sqrt x + 4}}dx} \hfill \\
\int {\frac{{dx}}
{{\sqrt x + 1}}} \hfill \\
u = \sqrt x \hfill \\
du = \tfrac{{dx}}
{{2\sqrt x }} = \tfrac{{dx}}
{{2u}} \Rightarrow dx = 2udu \hfill \\
\end{gathered}
$
$\displaystyle
2\int {\frac{{udu}}
{{u + 1}}} = 2\int {\frac{{u + 1 - 1}}
{{u + 1}}du = 2\int {1 - \frac{1}
{{u + 1}}du = 2u - 2\ln |u + 1| + C} }
$
Then substitute the square root of x back in for u and your set.