Integrate the following? #5x^2 e^(x^3) dx#

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Answer 1 · 2018-04-03T08:55:55

#5intx^2 e^(x^3) dx#

Let #x^3 = t#
#3x^2 dx = dt#

#5intx^2 e^(x^3) dx = 5int e^t dt/3#

#=> 5/3int e^t dt#

#=> 5/3 e^t +c#

#=> 5/3 e^(x^3) +c#

Answer 2 · 2018-04-03T09:00:49

#int5x^2e^u(du)/(3x^2)=5/3e^(x^3)+C#

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#int5x^2e^(x^3)dx#

Let #u=x^3, :. du=3v^2dx, :. dx=(du)/(3x^2)#

Let's substitute:

#int5x^2e^u(du)/(3x^2)=5/3inte^udu=5/3e^u+C#

Let's substitute back:

#int5x^2e^u(du)/(3x^2)=5/3e^(x^3)+C#