Math  /  Calculus

Question11+2xdx\int \frac{1}{1+2 x} d x

Studdy Solution
Substitute back the original variable xx in place of uu:
Since u=1+2xu = 1 + 2x, we have:
12lnu+C=12ln1+2x+C \frac{1}{2} \ln |u| + C = \frac{1}{2} \ln |1 + 2x| + C
The solution to the integral is:
12ln1+2x+C \boxed{\frac{1}{2} \ln |1 + 2x| + C}

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