Can someone find the indefinate integral of (dy/dx)= x (x -5)^1/2?

Question

anonymous · Answer

$$(2/15) (-5+x)^{3/2}(10+3x)$$

anonymous · Answer

Using substitution...
$$\Large \begin{array}{l}
\int {x{{(x - 5)}^{1/2}}} dx\
u = (x - 5)\
u + 5 = x\
\frac{{du}}{{dx}} = 1\
du = 1dx = dx\
\int {(u + 5)}  \cdot {u^{1/2}}du\
 = \int {{u^{3/2}} + 5{u^{1/2}}du} \
 = \int {{u^{3/2}}du}  + \int {5{u^{1/2}}} du\
 = \frac{{{u^{5/2}}}}{{5/2}} + \frac{{5{u^{3/2}}}}{{3/2}} + c\
 = \frac{{2{u^{5/2}}}}{5} + \frac{{10{u^{3/2}}}}{3} + c
\end{array}$$
Substitute back in for u and simplify.