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Aus Online Mathematik Brückenkurs 2

With the given variable substitution, u=x3 we obtain

du=x3dx=3x2dx 

and because the integral contains x2 as a factor, we can bundle it together with dx and replace the combination with 31du,

ex3x2dx=u=x3=eu31du=31eu+C 

Thus, the answer is

ex3x2dx=31ex3+C 

where C is an arbitrary constant.