Question

1/(1-x)^2求不定积分;x乘根号下(1+2x^2)求不定积分;x/根号下(1-x^2)求不定积分

Answer 1

1、∫dx/(1-x)^2

=∫d(x-1)/(x-1)^2

=-1/(x-1)+C

2、∫x√(1+2x^2)dx

=1/4*∫√(1+2x^2)d(1+2x^2)

=1/4*2/3*(1+2x^2)^(3/2)+C

=1/6*(1+2x^2)^(3/2)+C

3、∫xdx/√(1-x^2)

=-1/2*∫d(1-x^2)/√(1-x^2)

=-1/2*2*√(1-x^2)+C

=-√(1-x^2)+C