How can the integral of x^p exp(-tx) be solved for p=3/4, 5/4, and 7/4?

[gkannan16]

Homework Statement

Integral_0^1 x^p exp(-tx)dx where p=3/4. 5/4 and 7/4

Homework Equations

Can somebody tell me the final solution and the detailed procedure to get the final solution for this.

The Attempt at a Solution

I tried using gamma distribution and integration by parts but nothing worked.


Thanks
Kannan

 

[Avodyne]

This can be expressed in terms of the incomplete gamma function (see wikipedia), but otherwise cannot be done in closed form.