Integration by Substitution

**topher0805** · January 26th 2009, 12:51 PM

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...

**Danny** · January 26th 2009, 01:15 PM

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.

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