QuestionUsing the substitution: . Re-write the indefinite integral then evaluate in terms of .
Studdy Solution
STEP 1
1. We are given an integral with a substitution provided.
2. The substitution is .
3. We need to rewrite the integral in terms of and evaluate it.
STEP 2
1. Identify and perform the substitution.
2. Rewrite the integral in terms of .
3. Evaluate the integral in terms of .
4. Substitute back to express the result in terms of .
STEP 3
Identify the substitution: .
Calculate the derivative of with respect to :
This implies:
Solve for :
STEP 4
Substitute and into the integral:
Simplify the expression:
STEP 5
Evaluate the integral in terms of :
STEP 6
Substitute back to express the result in terms of :
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