∫e^x^1/3的不定积分?
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被积函数是e^[x^(1/3)]?
令x^(1/3)=t
x=t^3
dx=3t^2dt
∫e^x^1/3dx
=∫e^t3t^2dt
=3∫t^2de^t
=3t^2e^t-6∫te^tdt
=3t^2e^t-6te^t+6∫e^tdt
=3t^2e^t-6te^t+6e^t+c
=3x^(2/3)e^(x^1/3)-6x^(1/3)e^(x^1/3)+6e^(x^1/3)+c
令x^(1/3)=t
x=t^3
dx=3t^2dt
∫e^x^1/3dx
=∫e^t3t^2dt
=3∫t^2de^t
=3t^2e^t-6∫te^tdt
=3t^2e^t-6te^t+6∫e^tdt
=3t^2e^t-6te^t+6e^t+c
=3x^(2/3)e^(x^1/3)-6x^(1/3)e^(x^1/3)+6e^(x^1/3)+c
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