Question

1. интеграл dx/2+3x^2

2. интеграл 6z^2 da/(1-2z^3)^4

пж

Answer 1

$1)quad int frac{dx}{2+3x^2} =int frac{dx}{3(frac{2}{3}+x^2)}=frac{1}{3}cdot frac{1}{sqrt{2/3}}cdot arctg frac{x}{sqrt{2/3}} +C=\\= frac{1}{sqrt6} cdot arctg frac{sqrt3, x}{sqrt2} +C\\2)quad int frac{6z^2, dz}{(1-2z^3)^4}=\\=[, t=1-2z^3; ,; dt=-6z^2, dz; ,; dz=-frac{dt}{6z^2} ; ,; 6z^2, dz=-dt, ]=\\=-int frac{dt}{t^4} =-int t^{-4}dt=-frac{t^{-3}}{-3}+C=frac{1}{3t^3}+C=frac{1}{3(1-2z^)^3}+C$