Problems on Techniques of Integration

Since

$$\frac{3x^2 - 2x+1}{2x - 1} = \frac{3}{2} x - \frac{1}{4}+ \frac{3}{4} \frac{1}{(2x - 1)},$$

We have

$$\int \frac{3x^2 - 2x+1}{2x - 1}dx = \frac{3}{4} x^2 - \frac{1}{4}x+ \frac{3}{8}\ln\vert 2x-1\vert+ C\;.$$

Detailed Answer.

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