The questions requires a simple change of variable (which you do learn in high school). you start by letting as x becomes large so does t. but for x = 0 t = 1 hence the limits change.

do now you need to show that is the same as and the algebra involves in this is quiet fiddly.

firstly now multiply top and bottom by t I'm going to ommit a bit of algebra here but you should be able to work it out as .

For the next part you use the pervious result.

let

you integral is transformed to

note you don't need any advance knowledge of convergence / divergence to state that

Bobak