let
x= siny
dx=cosydy
∫dx/√(1-x^2)
=∫dy
=y
=arcsinx
let
z= tany
dz=(secy)^2dy
∫dx/(1+x^2)
=∫ dz
=z
=arctanx
∫ (3/(1+x^2) - 2/√(1-x^2) ) dx
=3∫dx/(1+x^2) - 2∫dx/√(1-x^2)
=3arctanx-2arcsinx + C
求3/(1+x^2)-2/(根号(1-x^2))的不定积分(有图)
let
x= siny
dx=cosydy
∫dx/√(1-x^2)
=∫dy
=y
=arcsinx
let
z= tany
dz=(secy)^2dy
∫dx/(1+x^2)
=∫ dz
=z
=arctanx
∫ (3/(1+x^2) - 2/√(1-x^2) ) dx
=3∫dx/(1+x^2) - 2∫dx/√(1-x^2)
=3arctanx-2arcsinx + C