Question

Помогите решить интегралы

Answer 1

$17)\; \; \int\limits^{\sqrt3}_0\, \frac{dx}{9+x^2}=\frac{1}{3}\cdot arctg\frac{x}{3}\Big |_0^{\sqrt3}=\frac{1}{3}\cdot (arctg\frac{\sqrt3}{3}-arctg0)=\frac{1}{3}\cdot \frac{\pi}{6}=\frac{\pi}{18}\\\\\\18)\; \; \int\limits^0_{-1}\, (x^3+2x)\, dx=(\frac{x^4}{4}+x^2)\Big |_{-1}^0=-\frac{1}{4}-1=-\frac{5}{4}$

$19)\; \; \int\limits^8_1\, \sqrt[3]{x^2}\, dx=\frac{3\, x^{5/3}}{5}\Big |_1^8=\frac{3}{5}\cdot (\sqrt[3]{8^5}-1)=\frac{3}{5}\cdot (2^5-1)=\frac{93}{5}$