感谢大家帮忙求下列函数的不定积分:求不定积分:(x+1)/3次根号下(3x+1)求不定积分:x^2/(1+x^2)^2求不定积分:1/x(x^10+1)求不定积分:根号x/1+3次根号下x求不定积分:arccostxdx求不定积分xf'(x)dx,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 04:31:12
![感谢大家帮忙求下列函数的不定积分:求不定积分:(x+1)/3次根号下(3x+1)求不定积分:x^2/(1+x^2)^2求不定积分:1/x(x^10+1)求不定积分:根号x/1+3次根号下x求不定积分:arccostxdx求不定积分xf'(x)dx,](/uploads/image/z/6954842-2-2.jpg?t=%E6%84%9F%E8%B0%A2%E5%A4%A7%E5%AE%B6%E5%B8%AE%E5%BF%99%E6%B1%82%E4%B8%8B%E5%88%97%E5%87%BD%E6%95%B0%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%28x%2B1%29%2F3%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8B%283x%2B1%29%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9Ax%5E2%2F%281%2Bx%5E2%29%5E2%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A1%2Fx%28x%5E10%2B1%29%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E6%A0%B9%E5%8F%B7x%2F1%2B3%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8Bx%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9Aarccostxdx%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86xf%27%28x%29dx%2C)
感谢大家帮忙求下列函数的不定积分:求不定积分:(x+1)/3次根号下(3x+1)求不定积分:x^2/(1+x^2)^2求不定积分:1/x(x^10+1)求不定积分:根号x/1+3次根号下x求不定积分:arccostxdx求不定积分xf'(x)dx,
感谢大家帮忙求下列函数的不定积分:
求不定积分:(x+1)/3次根号下(3x+1)
求不定积分:x^2/(1+x^2)^2
求不定积分:1/x(x^10+1)
求不定积分:根号x/1+3次根号下x
求不定积分:arccostxdx
求不定积分xf'(x)dx,其中f(x)的原函数为cosx/x
求不定积分xf'(2x)dx ,共中fx原函数为sinx/x
只剩第4题了,其它的都已解决。
感谢大家帮忙求下列函数的不定积分:求不定积分:(x+1)/3次根号下(3x+1)求不定积分:x^2/(1+x^2)^2求不定积分:1/x(x^10+1)求不定积分:根号x/1+3次根号下x求不定积分:arccostxdx求不定积分xf'(x)dx,
1.∫(x+1)/(3x+1)^(1/3)dx
设y=3x+1
dy/dx=d(3x+1)/dx=3
∫(x+1)/(3x+1)^(1/3)dx
=(1/3)∫[(y-1)/3]/y^(1/3)dy
=(1/9)∫[(y-1)y^(-1/3)]dy
=(1/9)∫[y^(2/3)-y^(-1/3)]dy
=(1/9)∫y^(2/3)dy-(1/9)∫y^(-1/3)]dy
=(1/9)(3/5)y^(5/3)-(1/9)(3/2)y^(2/3)+c
=(1/15)(3x+1)^(5/3)-(1/6)(3x+1)^(2/3)+c
2.∫x^2/(1+x^2)^2dx
设x=tanα
dx/dα=dtanα/dα=(secαx)^2
∫x^2/(1+x^2)^2dx
=∫(tanα)^2/(secα)^4*(secαx)^2 dα
=∫(tanα)^2/(secα)^2 dα
=∫(sinα)^2 dα
……
3.∫1/x(x^10+1)dx
4.∫[√x/1+x^(1/3)]dx
5.∫arccostxdx
6.∫xf'(x)dx,其中f(x)的原函数为cosx/x
7.∫xf'(2x)dx ,共中fx原函数为sinx/x
太多了,麻烦