Answer to Question #162034 in Calculus for Phyroe

Question

Evaluate the integral of z+2/z²+4z dz from -3 to 2

Answer 1

$\int\limits_{-3}^2 z+\frac{2}{z^2+4z}dz=\int\limits_{-3}^2 z+\frac{2}{z(z+4)}dz=\\ =\int\limits_{-3}^2 z+\frac{-0.5}{z+4}+\frac{0.5}{z}dz=\\ 0.5z^2-0.5\ln{(|z+4|)}+0.5\ln(|z|)|_{-3}^2=\\ -2.5-\ln{\sqrt{6}}+\ln{\sqrt{2}}-\ln{\sqrt{3}}=-2.5-\ln3$