Question

Integrate by combining direct and indirect substitution (which can be done in one ste if you like). (a) 1+ᵉ²ˣ

Answer 1

To integrate 1+e^(2x) using direct and indirect substitution, first set u = 2x and simplify the expression before integrating.

Step-by-step explanation:

To integrate the expression 1+e^(2x) using substitution, we can use the substitution u = 2x. This allows us to rewrite the expression as 1+e^u. Next, we can use the properties of the exponential function to simplify the expression further.

Let's go through the steps:

1. Set u = 2x
2. Find du/dx by differentiating u = 2x
3. Substitute u and du into the original expression
4. Integrate the simplified expression
5. Replace the variable u with the original variable x

By following these steps, we can integrate 1+e^(2x) using direct and indirect substitution.