e^x根号下e^x+1求不定积分;e^2x/(1+e^4x)求不定积分;e^根号x/根号x求不定积分.能回答几道就几道,

Question

e^x根号下e^x+1求不定积分;e^2x/(1+e^4x)求不定积分;e^根号x/根号x求不定积分.能回答几道就几道,

Answer 1

1、∫e^x√(e^x+1)dx
=∫d(e^x+1)√(e^x+1)
=2/3*(e^x+1)^(3/2)+C
2、∫e^2xdx/(1+e^4x)
=1/2*∫d^(e^2x)/[1+(e^2x)^2]
=1/2*arctan(e^2x)+C
3、∫e^(√x)dx/√x
=2*∫d(e^(√x))
=2e^(√x)+C