百科知识

教育/科学

求∫x^5sin5xdx.

2011-04-05 10:23:20s***
求∫x^5sin5xdx.：∫x^5sin(5x)dx =-1/5*cos5x[x^5-(x^5)''/5^2+(x^5)(4)/5^4]+1/5^2*sin?

最佳回答

  • ∫x^5sin(5x)dx =-1/5*cos5x[x^5-(x^5)''/5^2+(x^5)(4)/5^4]+1/5^2*sin5x[(x^5)'-(x^5)'''/5^2+(x^5)(5)/5^4]+C =-1/5*cos5x[x5-(20/25)x^3+(120/625)x]+1/25*sin(5x)[5x^4-(60/25)x+(120/625)]+C =-1/5*cos5x[x^5-(4/5)x^3+(24/125)x]+1/25*sin5x[5x^4-(12/5)x^2+(24/125)]+C.
    2011-04-05 14:02:37
  •   ∫x^5sin5xdx=(令5x=t)=(∫t^5sintdt)/(5^5)/5; ∫tsintdt=-∫tdcost=-tcost+∫costdt=sint-tcost, ∫x^5sin5xdx=(sin5x-(5x)^5co5x)/(5^6)+C; ----- ∫x^5sin5xdx=(-x^5cos5x+5∫x^4cos5xdx)/5; ∫x^4cos5xdx=(x^4sin5x-4∫x^3sin5xdx)/5; ∫x^3cos5xdx=(-x^3cos5x+3∫x^2cos5xdx)/5; ∫x^2cos5xdx=(x^2sin5x-2∫xsin5xdx)/5; ∫xsin5xdx=(sin5x-5xcos5x)/25; ∫x^5sin5xd=(25x^2sin5x-2(sin5x-5xcos5x))/125 =(-125x^3cos5x+3(25x^2sin5x-2(sin5x-5xcos5x)))/625 =(625x^4sin5x-4(-125x^3cos5x+3(25x^2sin5x-2(sin5x-5xcos5x))))/5^5; =(-5^4x^5cos5x+(625x^4sin5x-4(-125x^3cos5x+3(25x^2sin5x-2(sin5x-5xcos5x)))))/5^5+C; 。
      
    2011-04-05 14:05:42
    • 很赞哦！ (37)

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