Integral problem / mathematical induction

[Samme013]

View attachment 3411
Ok so i got step (a) and found that $\int_{0}^{\infty} \,d (x^0)*e^(-ax)dx=1/a$
But i do not get how i should go about starting the next steps using the info from the first step(have not done a similar problem before so i need to get a grasp on the method)

 

[Euge]

View attachment 3411
Ok so i got step (a) and found that $\int_{0}^{\infty} \,d (x^0)*e^(-ax)dx=1/a$
But i do not get how i should go about starting the next steps using the info from the first step(have not done a similar problem before so i need to get a grasp on the method)

Hi Samme013,

To solve (b), use integration by parts directly. Do not use the result in (a). To solve (c), use the result of part (b) and integration by parts.