Help with integrals

[sirii1403]

Can somebody please help me with this math problem with integrals? I really don´t know how to solve this and I´ve been sitting with this for days now. I´ve tried to solve it with partly integration where I choose the first part to be f(x) and the other part to be g´(x) and tried to use the product rule to solve them, but it´s becoming even more complex as I go by...I would be so happy if I can get some help or tips on how to solve this.

 

[DrPhil]

Can somebody please help me with this math problem with integrals? I really don´t know how to solve this and I´ve been sitting with this for days now. I´ve tried to solve it with partly integration where I choose the first part to be f(x) and the other part to be g´(x) and tried to use the product rule to solve them, but it´s becoming even more complex as I go by...I would be so happy if I can get some help or tips on how to solve this.


View attachment 3394

The tip you need is that the derivative of (1 + e^-kt) is -k e^-kt

Let \(\displaystyle u = 1 + e^{-kt}\),.... \(\displaystyle du = -k\ e^{-kt}\ dt\)

The integral becomes

\(\displaystyle \displaystyle -\dfrac{V_0}{k\ \sqrt{2}} \int u^{1/2}\ du \)