How do you integrate 2x3−3x2+x+1−2x+1?

1 Answer
Sasha P.
Sep 14, 2015

−x33+x22−12ln|2x−1|+C

Explanation:

We have to divide polinomials:

(2x3−3x2+x+1):(−2x+1)=−x2+x
−2x3+x2
−−−−
−2x2+x+1
+2x2−x
−−−−
1

2x3−3x2+x+1−2x+1=−x2+x+1−2x+1
∫2x3−3x2+x+1−2x+1dx=
=∫(−x2+x+1−2x+1)dx=
=−∫x2dx+∫xdx−∫dx2x−1=I
2x−1=t,2dx=dt,dx=dt2
I=−x33+x22−∫dt21t=
=−x33+x22−12ln|2x−1|+C

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