Find G (x)

Question

                    x
 Given G(x)=∫ln(2t +1)dt find G  (x)

                    1

 ln(2x + 1)
ln(2x + 1) - ln3
ln(2t + 1) + C
2/2x+1

Answer 1

If F(x) = ∫_{(from a to x)}f(t)dt, where a is a constant, then, by the Fundamental Theorem of Calculus, F'(x) = f(t).

 

So, if G(x) = ∫_{(from 1 to x)}ln(2t+1)dt,  then G'(x) = ln(2x+1).