f(x)=e^x/x,求∫f'(x)dx/1+f^2(x)?如题.
问题描述：
f(x)=e^x/x,求∫f'(x)dx/1+f^2(x)?
如题.
答
∫f'(x)dx/1+f^2(x)=∫df(x)/[1+f^2(x)]=arctanf(x)+c=arctan(e^x/x)+c
f(x)=e^x/x,求∫f'(x)dx/1+f^2(x)?
如题.
∫f'(x)dx/1+f^2(x)=∫df(x)/[1+f^2(x)]=arctanf(x)+c=arctan(e^x/x)+c