1. ## hard integral(i think)

integrate (4) / (4(x^1/2) + 4)

i believe i need a u substitution, but i am not sure

2. Originally Posted by whocares27
integrate (4) / (4(x^1/2) + 4)

i believe i need a u substitution, but i am not sure
Make the substitution $u = \sqrt{x} \Rightarrow dx = 2u \, du$.

3. Originally Posted by mr fantastic
Make the substitution $u = \sqrt{x} \Rightarrow dx = 2u \, du$.
After which use some simple algebra to get $2 \int 1 - \frac{1}{u+1} \, du$.

4. $
\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}
$

$
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.

5. thank you both so very much