integrals: ? (x^2 + 3)(3x^2 - 4x + 6) dx

[jenna89]

Could you help me with the problem below:

?(x^2+3)(3x^2-4x+6)dx

?x^2+1/2+1 dx+3?x dx + 3?x^2+1/2+1 dx-4?1x+6?x

?x^3/3 + 3x dx +3?x^3/3 dx-4?1x+6?x

thanks

 

[galactus]

Re: integrals

Are you trying partial fractions?.

\(\displaystyle \int\frac{x^{2}+3}{3x^{2}-4x+6}dx=\frac{4}{3}\int\frac{x}{3x^{2}-4x+6}dx+\int\frac{1}{3x^{2}-4x+6}dx+\frac{1}{3}\int dx\)

Can you think of a u-sub to try?. \(\displaystyle x=\frac{u+2}{3}\) may be helpful.