第2个回答 2010-04-18
1. =(1/3)*x^3+1/(1/2+1)*X^(1/2+1)+x+C
=(1/3)x^3+(2/3)x^(3/2)+xC
2. =-cosx-拉长f(xdsinx)
=-cosx-(xsinx-拉长f(sinxdx)
-cosx-xsinx-cosx+C
3. 设x=tant,则dx=sectdt
拉长f[1/(根号(x的平方+1))]=拉长f[(sect)^2/sect]dt
=拉长f(sect)dt=ln|sect+tant|+C
(sect)^2=1+(tant)^2=1+x^2
ln|sect+tant|+C=ln|x+根号(1+x^2)|+c
4. 拉长f(-x^2)dcosx=-x^2*cosx+拉长f(cosx)dx^2
=2*拉长f(xcosx)dx-x^2*cosx=2*拉长fxdsinx-x^2*cosx
=2xsinx+cosx-x^2*cosx+C