Reduction Formula :

[sareen]

Use integration by parts to prove the reduction formula:
? x^n e^x dx= x^n e^x - n?x^n-1 e^x dx

Then use the above to evaluate:
?x^3 e^x dx

 

[galactus]

Let \(\displaystyle u=x^{n}, \;\ dv=e^{x}dx, \;\ du=nx^{n-1}dx, \;\ v=e^{x}\)

Now, put it altogether using parts.

 

[sareen]

ok that will work