Họ nguyên hàm $\Large \int \left(\dfrac{x^2+2x+3}{x+1}\right)\mathrm{d

Họ nguyên hàm $\Large \int \left(\dfrac{x^2+2x+3}{x+1}\right)\mathrm{d}x$ bằng

• A.

  $\Large \dfrac{x^2}{2}+x-2\mathrm{ln}|x+1|+C$.

• B.

  $\Large x^2+x+2\mathrm{ln}|x+1|+C$.

• C.

  $\Large \dfrac{x^2}{2}+x-\dfrac{1}{(x+1)^2}+C$.

• D.

  $\Large \dfrac{x^2}{2}+x+2\mathrm{ln}|x+1|+C$.

Ta có $\Large  \int \left(\dfrac{x^2+2x+3}{x+1}\right)\mathrm{d}x$=$\Large \int \left(\dfrac{x^2+2x+1+2}{x+1}\right)\mathrm{d}x$=$\Large \int \left(\dfrac{(x+1)^2+2}{x+1}\right)\mathrm{d}x$=$\Large \int \left(x+1+\dfrac{2}{x+1}\right)\mathrm{d}x$=$\Large \dfrac{x^2}{2}+x+2\mathrm{ln}|x+1|+C$.