Question
Evalute : $\int \frac{x-1}{\sqrt{x+4}} d x$

Answer

$
\int \frac{x-1}{\sqrt{x+4}} d x=\int \frac{(x+4)-5}{\sqrt{x+4}} d x
$
$
\begin{aligned}
& =\int\left(\frac{x+4}{\sqrt{x+4}}-\frac{5}{\sqrt{x+4}}\right) d x \\
& =\int\left(\sqrt{x+4}-\frac{5}{\sqrt{x+4}}\right) d x \\
& =\int(x+4)^{\frac{1}{2}} d x-5 \int(x+4)^{-\frac{1}{2}} d x \\
& =\frac{(x+4)^{\frac{3}{2}}}{\left(\frac{3}{2}\right)}-5 \cdot \frac{(x+4)^{\frac{1}{2}}}{\left(\frac{1}{2}\right)}+c
\end{aligned}
$
$2{ }_3^3$ $=\frac{2}{3}(x+4)^{\frac{3}{2}}-10 \sqrt{x+4}+c$.

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