Question

Given G of x equals the integral from 1 to x of the natural logarithm of the quantity 2 times t plus 1, dt, find G '(x)

ln(2x + 1)
ln(2x + 1) − ln3
ln(2t + 1) + C
2 divided by the quantity 2 times x plus 1

my answer is ln(2x+1) but I dont think its right

Answer 1

review the 2nd Fundamental Theorem of Calculus.

If ∫ln(2t+1) dt = f(t), then

G(x) = f(x) - f(1)
So, naturally, G'(x) = ln(2x+1)

the 2nd integral is just