Prove that ∫(1,∞) 1/x dx=∞

英语翻译Prove that the curves y=x^3 and y=(x+1)/(x^2 +4) have ex 1：Prove that if x is a positive integer that is not divisibl 1-∫[0,+∞]e^-x dx=? ∫ x/(1+X^2)dx= ∫dx/x(1+x) 微积分∫[-∞, ∞]x^2*(1/2)*e^(-|x|)dx|=2∫[0, +∞]x^2*(1/2)*e^(-x)dx 广义积分∫（0～+∞）dx/1+x^2 dx 怎么求? 计算[1/(1+x^2)]dx -∞ 证明∫（0,+∞）dx/(1+x^4)=∫（0,+∞）x^2/(1+x^4)dx.并求值 ∫1/(1-x^4)dx=? ∫1/1+x²dx= given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0