Question

solve using u-substitution? @michele_laino

Answer 1

here, we can make this variable change:
\(\large 3+e^x=u\)

Answer 2

du/dx would equal e^x right?

Answer 3

yes!

Answer 4

k, so it would simplify to
right?

Answer 5

correct! Nevertheless better if we don't write the limits of integration at this step

Answer 6

okay, and then that's \(\large \ln|3+e^x|\)

Answer 7

right?

Answer 8

and then solve for the interval?

Answer 9

correct! since the function \(3+e^x\) is always positive, we can eliminate the symbol of absolute value

Answer 10

okay

Answer 11

I got approx 0.954

Answer 12

yes! We can do this computation:
\[\Large \ln \left( {3 + {e^2}} \right) - \ln \left( {3 + 1} \right) = ...?\]

Answer 13

Thank you for the help!

Answer 14

:)