How do you integrate #int x e^ sqrtx dx # using integration by parts?
1 Answer
Explanation:
First, we use substitution.
Let
Then, substituting, we have
Next, we apply integration by parts three times, using the formula
Let
Then
Applying the formula:
Integration by Parts 2:
Focusing on the remaining integral, let
Then
Applying the formula:
Integration by Parts 3:
Again, focusing on the remaining integral, let
Then
Applying the formula:
Substituting our result into the second integration by parts step, we obtain
Substituting this into the first integration by parts step, we obtain
Finally, we substitute