Question

Evaluate:

$\int \frac{x^4+4}{x^2-2x+2}dx$

• A. $\frac{x^3}{2}+x^2+2x+C$
• B. $\frac{x^3}{3}+x^2+2x+C$
• C. $\frac{x^3}{3}+x^2+x+C$
• D. $\frac{x^3}{3}+x^2-2x+C$

Answer 1

The correct option is B $\frac{x^3}{3}+x^2+2x+C$

Given,

$\int \frac{x^4+4}{x^2-2x+2}dx$

as $(x^2+2x+2)(x^2-2x+2)=x^4+4$

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

$=\int (x^2+2x+2)dx$

$=\int x^{2}dx+\int 2xdx+\int 2dx$

$=\frac{x^3}{3}+x^2+2x+C$