Question

Find the integral.

Answer 1

\[\int\limits \frac{x-15}{x^2 +1}\]

Answer 2

I believe we can split them up into.

Answer 3

\[\int\limits \frac{x}{x^2 +1} - \int\limits \frac{15}{x^2 +1}\]

Answer 4

\[\int\limits \frac{x}{x^2 +1} - 15\int\limits \frac{1}{x^2 +1}\]

Answer 5

\(x^2+1\) doesn't have a partial fraction decomposition in \(\mathbb{R}\). Hmm.

Answer 6

so I cannot do what I was doing?

Answer 7

I'm saying that this looks more complicated than it first appeared.

Answer 8

Ok...

Answer 9

Polynomial long division?

Answer 10

wouldn't the left side just be a log, and the right side be an arctan?

Answer 11

For left:

u = x^2+1
1/2 du = x

For right:

u = x
a = 1

Answer 12

I think you have it.

Answer 13

\[\frac{1}{2} \int\limits \frac{du}{u} - 15 \int\limits \frac{du}{u^2 +a^2}\]

Answer 14

Wait..

Answer 15

\(du=2x\). Your right hand side isn't equal to the original.

Answer 16

Oh, looked at the wrong one. Nevermind.

Answer 17

\[\frac{1}{2} \ln|u| - 15 * \frac{1}{1}\arctan(\frac{x}{1}) + c\]

Answer 18

\[\frac{1}{2} \ln|x^2+1| - 15 \arctan(x) + c\]

Answer 19

:D

Answer 20

Looks right to me.

Answer 21

LEts see what Wolfram has to say.

Answer 22

yup woot! :) ty

Answer 23

You're welcome!