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

2 Answers
Apr 3, 2018

#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#

Apr 3, 2018

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

Explanation:

.

#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#