#### To determine

Evaluate the integral of ∫x2×ex3dx.

#### Answer

ex33+c.

#### Explanation

**Given:** ∫x2×ex3dx.

Consider y=∫x2× ex3dx

Substitute the value of t=x3 then,

dt=3x2dx

x2dx=dt3

And,

∫x2⋅ex3dx=∫et3dt=13∫etdt=13et+c

Now put the value of t in the above equation.

=13ex3+c

**Conclusion:** Hence, the integral of ∫x2×ex3dx is ex33+c.