急！求不定积分 高数作业，要详细过程！好的有加分O(∩_∩)O谢谢

1. ∫x^2dx/(9+x^2)=∫[1-9/(9+x^2)]dx=x-3∫dx/3/(1+(x/3)^2)=x-3arctan(x/3)+C

2. ∫(x^2+1)dx/[(x+1)^2*(x-1) ]=∫[(x+1)^2-2(x-1)-2]dx/[(x+1)^2(x-1)]
=∫dx/(x-1)-2∫dx/(x+1)^2-∫[(x+1)-(x-1)]dx/[(x+1)^2(x-1)]
=ln|x-1|+2/(x+1)-(1/2)∫[(x+1)-x-1)]dx/[(x+1)(x-1)] +∫dx(x+1)^2
=ln|x-1|+2/(1+x)-(1/2)ln|x-1|+(1/2)ln|x+1|-1/(1+x)+C
=(1/2)ln|x-1|+1/(1+x)+(1/2)ln|x+1|+C

3. ∫xdx/x^2+2x+2 =(1/2)∫(2x+2)dx/(x^2+2x+2) -∫dx/[(x+1)^2+1]
=(1/2)ln|x^2+2x+2|-arctan(x+1)+C

4. ∫dx/[x*√(2x+1)]=(1/2)∫xd(2x+1)/√(2x+1)=∫xd√(2x+1)=x√(2x+1)-∫(2x+1)dx
=x√(2x+1)-(1/2)*(2/3)√(2x+1)^3+C

5. ∫[(√(x+1)-1/(√x+1)+1 ]dx=∫[√x+1-1]^2dx/[√(x+1)^2-1] =∫[x+2-2√(x+1)]dx
=x^2/2+2x-2*(2/3)√(x+1)^3+C

6. ∫dx/∫√(1+e^x )=∫e^(-x/2)dx/√[1+e^(-x)]=-2∫de^(-x/2)/√{1+[e^(-x/2)]^2}
=-2arcsin [e^(-x/2)] +C