Hi!
[tex]\frac{x^3}{(a^2)-(x^2)}[/tex]
First remove parenthesis.
[tex]\frac{x^3}{a^2-x^2}[/tex]
Factor [tex]a^2-x^2[/tex] or [tex](x+a)(a-x)[/tex]
[tex]=\frac{x^3}{(a+x)(a-x)}[/tex]
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-Charlie
Note that a^2 is a constant. Thus, the given expression (x^3)/(a^2)-(x^2) is equivalent to (1/a^2)x^3 = x^2.
x^4
Integrating the first term with respect to x results in (1/a^2)---------
4
x^3
and integrating the second with respect to x results in -------- + C
3
where C is the constant of integration. Thus, the overall indefinite integral is
x^4 x^3
(1/a^2)--------- + ----------- + C
4 3
