∫ln(x+√(x^2-1)dx,

网友回答

很高兴为您解答,解题步骤如下,
∫ln(x+√(x^2-1)dx,(图1)
 
 
或者如果不要过程,我们可以：
∫ln(x+√(x^2-1)dx,(图2)======以下答案可供参考======
供参考答案1:
令x=cosa， 则x+√(x^2-1=√2sin(a+45)/2
接下来就会了吧
供参考答案2:
令y=ln(x+√(x^2-1))
=>e^y = x+√(x^2-1)
已知ln(x+√(x^2-1))+ln(x-√(x^2-1))=ln(xx-xx+1)=0
=>-y = ln(x-√(x^2-1))
=>e^-y = x-√(x^2-1)
=>x = 1/2*(e^y+e^-y)
=>∫ln(x+√(x^2-1)dx=∫ydx=1/2*(∫y(e^y-e^-y)dy
已知：∫ye^ydy=∫yd(e^y