Math Help - Integration by Substitution

1. Integration by Substitution

My teacher wants me to solve this by substitution:

$\int^7_0 \frac{x}{\sqrt{1+5x}}$

My work so far:

$u = 1+5x$

$du = 5$

$x = \frac{u-1}{5}$

$dx = \frac{1}{5}$

Not sure where to go from here...

2. Originally Posted by topher0805
My teacher wants me to solve this by substitution:

$\int^7_0 \frac{x}{\sqrt{1+5x}}$

My work so far:

$u = 1+5x$

$du = 5$

$x = \frac{u-1}{5}$

$dx = \frac{1}{5} \,du$ don't forget this du

Not sure where to go from here...
Switch your limits $x = 0, u = 1,\;\;\;x = 7, u = 36$and put in the pieces

$\frac{1}{25}\, \int_1^{36} \frac{u-1}{\sqrt{u}}\, du$

now expand and integrate.