Last Integrating Question

[yohanson77]

Hello,
Left this one out as I can't work out the process, please be easy on me I've only been doing this for a week.

integral(8 x^2-3 x+19/(x^2+3) (x-1), x)

Thank you in advance

yohanson77

 

[galactus]

Try partial fractions.

\(\displaystyle \L\\\frac{Ax+B}{x^{2}+3}+\frac{C}{x-1}\)

\(\displaystyle \L\\(Ax+B)(x-1)+C(x^{2}+3)=8x^{2}-3x+19\)

\(\displaystyle \L\\Ax^{2}-Ax+Bx-B+Cx^{2}+3C=8x^{2}-3x+19\)

Equating coefficients gives the system:

\(\displaystyle \L\\A+C=8\)
\(\displaystyle \L\\-A+B=-3\)
\(\displaystyle \L\\-B+3C=19\)

Solve and find your PFD

Then integrate each term.