Boltzmann maxwell equation: int 4Π(m/2Πkt)^3/2v³ e^-mv²/2kt

[svoboda1]

Boltzmann maxwell equation: int 4Π(m/2Πkt)^3/2v³ e^-mv²/2kt

[FONT=&quot]Hi everyone, [/FONT]

[FONT=&quot]I'm trying to solve the bolzman equation to find the average speed [/FONT]

[FONT=&quot]integral between 0 and +infinity : ∫4Π(m/2Πkt)^3/2v³ e^-mv²/2kt [/FONT]

[FONT=&quot]with the substitution u = mv²/2kt [/FONT]

[FONT=&quot]I know we can do it with other substitution but we have to use this... [/FONT]
[FONT=&quot]my final answer is 4/√Π * ∫ u^3/2 e^-u du/√u [/FONT]

[FONT=&quot]the teacher said : ∫u^3/2 e^-u du = 3/4*√Π (integral between o and +infinity) [/FONT]
[FONT=&quot]My probem is that I can’t simplify my integral because I have the term du/√u and if I solve it I obtain ∫ u. e^-u du and I can’t symplify ... [/FONT]
[FONT=&quot]can someone show me if I did a mistake?? thank you !!![/FONT]