分类：教育/科学-理工学科-数学
问题：求∫x^5sin5xdx. 
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.