Question

nguyên hàm: \(\int\dfrac{x^2+2x}{2x-1}dx\)

Answer 1

\(\int\dfrac{x^2+2x}{2x-1}dx\\ =\int\left(\dfrac{1}{2}x+\dfrac{5}{4}+\dfrac{5}{8x-4}\right)dx\\ =\dfrac{x^2}{4}+\dfrac{5}{4}x+\dfrac{5}{8}\ln\left|2x-1\right|+C\)

Answer 2

\(\int\dfrac{x^2+2x}{2x-1}=\int\dfrac{1}{2}\cdot\dfrac{2x^2+4x}{2x-1}\)

\(=\dfrac{1}{2}\cdot\int\dfrac{2x^2-x+5x-2,5+2,5}{2x-1}\)

\(=\dfrac{1}{2}\cdot\int x+2,5+\dfrac{2.5}{2x-1}\)

\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2}x^2+2,5x+\dfrac{2.5}{2}\cdot ln\left|x-\dfrac{1}{2}\right|\right)\)