Question
Use the substitution
to find the following indefinite integral. Check your answer by differentiating.
Ask by Moran Mann. in the United States
Mar 12,2025
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To solve the integral
using the substitution
, first, we need to find
:
- Differentiate
:
Now rewrite the integral in terms of
:
- Now, integrate:
- Substitute back
:
Thus, the solution to the integral is:
Now, let’s check our answer by differentiating the result:
- Differentiate
:
This matches the integrand
. Therefore, the original integral evaluates to: