I need help with finding the intergral of (x^n)(e^x)

I need help with finding the intergral of (x^n)(e^x). I already did for 1,2 and 3. I found out that x^n*e^x times the intergral of (x^n-1)e^x. Is there anyway I can genralize for all n s with out having an integral.

Post this in the homework section "Calculus and Beyond" and you are much more likely to get an answer.

Easy, use integration by part, show the following relationship
$$\int x^n e^x dx = x^ne^x -n\int x^{n-1}e^x dx$$

Then use the recurrence relation on $$\int x^{n-1} e^x dx$$.
You will get
$$\int x^{n} e^x} dx = \sum _{i=0} ^{n} (-1)^i\frac{n!}{(n-i)!}e^xx^{n-i}$$

Last edited:
Gib Z
Homework Helper
chanvincent is correct. when its the same integral with e^NEGATIVE x, its a nice definiton for the gamma function.