Integrate X^5e^(1-x^6)dx Help?
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∫x^5.e^(1-x^6)dx
Let u = 1 - x^6
du/dx = -6x^5.
dx = du/(-6x^5)
∫x^5e^u.dx
Replace ''dx'' as ''du/(-6x^5)''
∫x^5.e^u.[du/(-6x^5)]
-1/6∫x^5.e^u.[du/x^5]
x^5 cancelled out
-1/6∫e^udu
-(1/6)e^u + K
Remember u = 1 - x^6
:-'-: ∫x^5e^(1 - x^6)=~> -(1/6)e^(1 - x^6) + K..//
Let u = 1 - x^6
du/dx = -6x^5.
dx = du/(-6x^5)
∫x^5e^u.dx
Replace ''dx'' as ''du/(-6x^5)''
∫x^5.e^u.[du/(-6x^5)]
-1/6∫x^5.e^u.[du/x^5]
x^5 cancelled out
-1/6∫e^udu
-(1/6)e^u + K
Remember u = 1 - x^6
:-'-: ∫x^5e^(1 - x^6)=~> -(1/6)e^(1 - x^6) + K..//
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