Question

∫x+1/2x-x2+2 dx

Answer 1

Pls guys help me solve this problem i have Exams tomorrow.
pls

Answer 2

do you know how to long divide polynomials?

Answer 3

yes

Answer 4

That's pretty much what you have to do here, so that your integral becomes (-x+3) - (1/(x+1)). Then you can solve the integral.

Answer 5

hold up a minute, I think I messed it up, give me a minute or two.

Answer 6

ok

Answer 7

the denominator is 2x-x square + 2

Answer 8

it looks like you separate by partial fractions \[x+1 =( Ax +B)/(2x-x^2+2)\]. Because the deonimator is a irreducible quadratic eq. Once you solve for A and B, then you should have a differentiable eq.

Answer 9

sorry about the mix up before I jumped into a bad conclusion too fast.

Answer 10

\[\int\limits \left(2+\frac{1}{2 x}+x-x^2\right) \, dx = 2 x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{\text{Log}[x]}{2} \]

Answer 11

hello

Answer 12

is that the final ans.

Answer 13

from robtobey,
Yes.

Another version is the result factored:
\[\frac{1}{6} \left(12 x+3 x^2-2 x^3+3 \text{Log}[x]\right) \]

Answer 14

You can check the result of the integration by taking the derivative of the result with respect to x.