Question

Integrate (x^3)/(a^2)-(x^2) ?

Answer 1

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

Answer 2

Hi!

$\frac{x^3}{(a^2)-(x^2)}$

First remove parenthesis.

$\frac{x^3}{a^2-x^2}$

Factor $a^2-x^2$ or $(x+a)(a-x)$

$=\frac{x^3}{(a+x)(a-x)}$

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-Charlie