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Integration By Parts

In this example, there is a product of x^2 and cosx dx in the integrand.

Does simple u-substitution method work for this example?

In order to use the simple u-substitution method, the relationship between two functions must be the original and its derivative each other except for constants.

Unfortunately, x^2 cannot be the derivative of cosx or cosx cannot be the derivative of x^2 either.  Therefore, we cannot use the u-substitution method here.

Then Let’s try to use Integration by parts method.