Question

求下列函数的微积分，共4题，写过程，高分悬赏

(1)y=x的平方+x的开二次方+1
(2)y=sinx-xcosx
(3)y=1/(根号（x的平方+1）)
(4)y=(x的平方)*(sinx)

Answer 1

答案如下图

Answer 2

(1)y=x^2+√x+1
dy=[2x+1/(2√x)]dx
(2)y=sinx-xcosx
dy=(cosx-cosx+xsinx)dx=(xsinx)dx
(3)y=1/[√（x^2+1）]
dy=-x（x^2+1)^(-1.5)dx
(4)y=(x^2)*(sinx)
dy=(2xsinx+x^2cosx)dx

Answer 3

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