Question

nguyên hàm: \(\int\dfrac{x^3+x^2}{x^2+6x+5}dx\)

Answer 1

Ta có:

\(\int\dfrac{x^3+x^2}{x^2+6x+5}dx=\int\dfrac{x^2}{x+5}dx\)

\(=\int\left(x-5+\dfrac{25}{x+5}\right)dx=\dfrac{1}{2}x^2-5x+25ln\left|x+5\right|+C\)