How do I know when to integrate using by parts or by substitution?

When integrating a function which can be defined as a combination of two functions, it can be difficult to tell whether or not to use by parts. We can spot when to use by parts if we look at the composite function, split it into an f(x) and g(x) and check if the functions has different forms of x, i.e normal polynomial, trigonometric and logarithmic.For example: Determine \xsin(x)dx (\ = integral)Let f(x) = x, g(x) = sin(x) These functions are of different forms so we apply the by parts formula (uv - \v'u) where f(x) = u and g'(x) = v-xcos(x) - -cos(x)dx = -xcos(x) + sin(x) + c

Answered by Eesa K. Maths tutor

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