Question

Integral x^2+2/ x+1 dx

Answer 1

Step-by-step explanation:

We have,

$\int \frac{ {x}^{2} + 2 }{x + 1} dx$

$= \int \frac{ {x}^{2} + 2x + 1 - 2x + 1}{x + 1} dx$

$= \int \frac{ {x}^{2} + 2x + 1 }{x + 1} dx + \int \frac{ - 2x + 1}{x + 1} dx$

$= \int \frac{ {(x + 1)}^{2}}{x + 1} dx + \int \frac{ - 2x - 2 + 3}{x + 1} dx$

$= \int (x + 1) dx + \int \frac{ - 2x - 2 }{x + 1} dx + \int \frac{3}{x + 1} dx$

$= \int (x + 1) dx + \int ( - 2)dx + \int \frac{3}{x + 1} dx$

$= \frac{ {x}^{2} }{2} + x - 2x + 3 \ln(x + 1) + C$

$= \frac{ {x}^{2} }{2} - x + 3 \ln(x + 1) + C$