Question

d) integrate x2 +x2 +5/(x2+4) (x+1) dx

Answer 1

$\int \left(x^2+x^2+\frac{5}{x^2+4}(x+1)\right)dx=2\int x^{2}dx+5\int \frac{x+1}{x^2+4}dx=$

$2\frac{x^{2+1}}{2+1}+5\int \frac{x}{x^2+4}dx+5\int \frac{1}{x^2+4}dx=$

$=\frac{2x^3}{3}+\frac{5}{2} \int{\frac{d(x^2+4)}{x^2+4}}+5 \int{\frac{1}{x^2+2^2}}dx=$

$=\frac{2x^3}{3}+\frac{5}{2}log|x^2+4|+\frac{5}{2}arctan(\frac{x}{2})+C.$