早教吧作业答案频道 -->数学-->
∫x^5/(x^3+1)^(1/4)dx
题目详情
∫x^5/(x^3+1)^(1/4)dx
▼优质解答
答案和解析
令t=(x^3+1)^(1/4) x=(t^4-1)^(1/3) dx=(4/3)*(t^4-1)^(-2/3)*t^2
原式=∫(t^4-1)^(5/3)*(4/3)*(t^4-1)^(-2/3)*t*dt
=4/3*∫(t^5-t)dt
=4/3*[(t^6)/6-(t^2)/2]+C
=(2t^6)/9-(2t^2)/3+C
=2/9*(x^3+1)^(3/2)-2/3*(x^3+1)^(1/2)+C
原式=∫(t^4-1)^(5/3)*(4/3)*(t^4-1)^(-2/3)*t*dt
=4/3*∫(t^5-t)dt
=4/3*[(t^6)/6-(t^2)/2]+C
=(2t^6)/9-(2t^2)/3+C
=2/9*(x^3+1)^(3/2)-2/3*(x^3+1)^(1/2)+C
看了 ∫x^5/(x^3+1)^(...的网友还看了以下：