Solving a polynomial integral.

[standardflop]

I can't seem to solve this integral,
$$\int \frac{x^2+x+1}{(x^2+1)(x+1)}dx$$
Maple, however, solves is exact quiet easily, and i'd really like to see how this can be done "by hand".

Best regards.

 

[EmilK]

I can't seem to solve this integral,
$$\int \frac{x^2+x+1}{(x^2+1)(x+1)}dx$$
Maple, however, solves is exact quiet easily, and i'd really like to see how this can be done "by hand".

Best regards.

Simplification. Integration by parts.

http://online.math.uh.edu/HoustonACT/videocalculus/index.html

Scroll down to number 34 and view the video for a tutorial.

 

[arildno]

Hmm..I hardly see how integration by parts is the simplest way of doing this.
A much easier way is to use partial fractions decomposition.
This is done by trying to find numbers A,B,C so that we have:
$$\frac{x^{2}+x+1}{(x^{2}+1)(x+1)}=\frac{Ax+B}{x^{2}+1}+\frac{C}{x+1}$$