QuestionChoose for integration by parts in . Recall: .
Studdy Solution
STEP 1
Assumptions1. We are using the method of integration by parts to solve the integral.
. The integration by parts formula is .
3. We need to choose and such that the integral of is easier to compute than the original integral.
STEP 2
We have the integral . We need to choose and .
STEP 3
The general guideline for choosing in integration by parts is LIATE, which stands for Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential functions, in that order of preference.
STEP 4
In our integral, we have an algebraic function and an inverse trigonometric function .
STEP 5
According to the LIATE rule, we prefer inverse trigonometric functions over algebraic functions. Therefore, we choose .
STEP 6
After choosing , we assign the rest of the integral to . Therefore, .
STEP 7
So, the choices for and in the integration by parts formula are and .
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