Question 1198799
<pre>
{{{int( (x^2)/(x^3 + 4), dx,0,5)}}}

Notice that the numerator has the same power of x, (2), as the derivative of
the denominator {{{x^3+4}}} has. The derivative of the denominator is {{{3x^2}}}.

So the numerator can be made into the derivative of the denominator by inserting
a 3 factor in the numerator and multiplying by 1/3 on the outside of the
integral sign.

{{{expr(1/3)int( (3x^2)/(x^3 + 4), dx,0,5)}}}

We use the formula {{{int(du/u)}}}{{{""=""}}}{{{ln(u)}}}{{{""+""}}}{{{C}}}

{{{expr(1/3)ln(x^3+4)}}}{{{matrix(3,1,"|5","|  ","|0")}}}{{{""=""}}}{{{expr(1/3)(ln(5^3+4)-ln(0^3+4)^"")}}}{{{""=""}}}{{{expr(1/3)(ln(129)-ln(4)^"")}}}.

That is approximately 1.157839348

Edwin</pre>