Question: Integration by parts

 

ok,

my first quations is: How can I get  V(F(x), G(x)) in the last expression in the below picture evaluated at the end point t and T. 

The solution should be a vertical line to the right-hand side of the expression

 

My second quation is: Is there any way I can sequentialy solve the problem without having to manually rewrite the equations

 

 

 

My third question is: How does the last expression in the previous picture relates to the last expression in picture below and is there a way to combine the two?

 

 

 

 

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