Indefinite integral?

• February 15th 2008, 07:29 AM
TrueToHeart
Indefinite integral?
how do you evaluate the following indefinite integrals?

(1 + √(2s-1)) /√(2s-1) ds

i know the answer to this is 1/2(1+√(2s-1))² + c but still don't get it. :S
and

(x²+3)^7 (x³-8x) dx
• February 15th 2008, 08:36 AM
Peritus
$\int {\frac{{1 + \sqrt {2s - 1} }}
{{\sqrt {2s - 1} }}} ds = \int {1 + } \frac{1}
{{\sqrt {2s - 1} }}ds = s + \left( {2s - 1} \right)^{{\raise0.7ex\hbox{1} \!\mathord{\left/
{\vphantom {1 2}}\right.\kern-\nulldelimiterspace}
\!\lower0.7ex\hbox{2}}} + C$

The answer is given in an equivalent form:

$0.5\left( {1 + \sqrt {2s - 1} } \right)^2 = 0.5\left( {1 + 2\sqrt {2s - 1} + 2s - 1} \right) = \sqrt {2s - 1} + s
$

Quote:

(x²+3)^7 (x³-8x) dx
I'm not sure how to understand this?