(14)int(e^x)/(1+e^x)dx;

例4.求int(dx)/(1+e^x).例4.求$\int\frac{dx}{1+e^{x}}$.

140.(2023·安徽)计算定积分int_(-1)^1((1-e^x)/(1+e^x)+xe^x)dx.140.(2023·安徽)计算定积分$\int_{-1

( 单选题 ) int dfrac ({e)^x}(1+{e)^2x}dx=_________int dfrac ({e)^x}(1+{e)^2x}dx=int

int((1)/(sqrt(x))-e^x)dx= ().A. $\sqrt{x}-e^{x}+C$B. $2\sqrt{x}-e^{x}+C$C. $\sqr

(int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx= ()-|||-__

14、计算定积分int_(1)^e(ln^2x)/(x)dx.14、计算定积分$\int_{1}^{e}\frac{\ln^{2}x}{x}dx$.

(int )_(1)^(e^2)dfrac (ln x)(sqrt {x)}dx= __

设 int dfrac (f(x))(x)dx=(e)^x+C ，则int dfrac (f(x))(x)dx=(e)^x+Cint dfrac (f(x))(

[例3] (int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx

全微分方程 (1+e^x/y)dx+e^x/y(1-(x)/(y))dy=0 的通解为()A. $x-ye^{x/y}=C$B. $x+ye^{x/y}=C$C