Question

Find the antiderivative for the function f(x) = (x – 11)(x + 13).

Please help

Answer 1

Expanding the product is simple enough:

`(x-11)(x+13)=x^2+2x-143`

Then

`\displaystyle\int(x-11)(x+13)\,\mathrm dx=\frac{x^3}3+x^2-143x+C`

We could also use a subsitution like
`u=x-11`, so that
`u+24=x+13` and
`\mathrm du=\mathrm dx`:

`\displaystyle\int u(u+24)\,\mathrm du=\int(u^2+24u)\,\mathrm du=\frac{u^3}3+12u^2+C`

`\implies\displaystye\int(x-11)(x+13)\,\mathrm dx=\frac{(x-11)^3}3+12(x-11)^2+C`

(which is differs from the first result by a constant, so it's still valid)

Answer 2

1/3x^3+x^2-143x+c

Explanation:

i got it right on the test