Question

evaluate the integral (3+2x-x^2)^(3/2) dx

Answer 1

\[\int\limits_{}^{} \sqrt[]{(3+2x-x^2)^3} dx\]

Now, let's get rid the the square root by writing the inside as something squared.
To do that we will need to complete the square and choose a trig sub such that the inside is just something square.

Answer 2

Do you know how to complete the square?

Answer 3

The inside is
\[-x^2+2x+3\]
\[=-(x^2-2x)+3\]
\[=-(x^2-2x+?)+3+?\]
What do we need to replace question with so that we can write that one part as something square.
Like this:
\[=-(x- \text{ blah} )^2+3+?\]