Question

x²+5x+3/x²+3x+2 (x ≠ -2, -1),Integrate it with respect to x.

Answer 1

Answer:

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Answer 2

Answer:

$\frac{x^3}{3} +5\frac{x^2}{2} -3\frac{1}{x} +3\frac{x^2}{2} + 2x + C$

Step-by-step explanation:

Here, we have Equation

$\int (x^{2}  + 5x +\frac{3}{x^2}+3x+2)dx$

Now, we integrated with respect to x

$=\int x^{2} dx +\int 5x dx+\int \frac{3}{x^2} dx +\int 3x dx + \int 2 dx\\=\int x^{2} dx +5\int x dx+3\int \frac{1}{x^2} dx +3\int x dx +2 \int  dx\\=\frac{x^3}{3} +\frac{x^}{2} +(\frac{-1}{x}) +\frac{x^2}{2} + 2x  + C \\=\frac{x^3}{3} +5\frac{x^}{2} -3\frac{1}{x} +3\frac{x^2}{2} + 2x + C$

where C is the constant of integration.