MathAnalysisCalculusIntegrals

Integration by parts

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Let's consider the following integral:

$\int \sin(x) \ln(\cos(x)) \ dx$

Which of the following combinations would yield an easier integral to solve?

Select one option from the list

u = \sin(x) \qquad \qquad \quad \ \ \text{and} \quad dv = \ln(\cos(x)) dx

u = \sin(x) \ln(\cos(x)) \quad \text{and} \quad dv = 1 \cdot dx

u = \ln(\cos(x)) \qquad \quad \ \ \ \text{and} \quad dv = \sin(x) dx

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