Help with integrating without substitution (C4)

Does the differential of the bottom bracket help you spot something relative to the top?

Anyone else know? =/ I need to get this done today and this is only the first question in the work (they are all similar basis), and I am out all day tomorrow at an awards ceremony for young person of the year so can't really get it done as going out to celebrate after ... (I know last minute! xD)

If you differentiate the bottom, what does that give you.

You should also know the $\frac{d}{dx} ln(f(x)) = \frac{f'(x)}{f(x)}$

Here's my method of doing this;

$\int \frac{x^2 }{1+x^3 } dx = \int \frac{f'(x) }{f(x) } dx = ln|f(x)|$

$[br]f(x) = 1+x^3[br]f'(x)= 3x^2[br][br]= \dfrac{1}{3} \int \dfrac{3x^2 }{1+x^3 } dx[br]= \int \dfrac{f'(x) }{f(x) } dx[br]= ln \ |f(x)| \ + c[br]= \dfrac{1}{3} ln|1+x^3 | +c$

... I am confused. You are doing dy/dx... which is differentiation, and I am integrating in my quesiton??

Integration is the inverse of differentiation.

If you look at the solution brecon's given, you'll see he uses what I've said.

Here's my method of doing this;