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These techniques are combined when the integrand can be split into a product where one factor simplifies upon differentiation (for integration by parts) and the other factor is integrable only via substitution. This often occurs with polynomials multiplied by composite functions like $\sqrt{ax^n+b}$.

Conditions: The integrand is a product of two distinct types of functions.; One part reduces nicely when differentiated.; The other part requires a u-substitution to find its antiderivative.

These techniques are combined when the integrand can be split into a product where one factor simplifies upon differentiation (for integration by parts) and the other factor is integrable only via substitution. This often occurs with polynomials multiplied by composite functions like $\sqrt{ax^n+b}$.

Conditions: The integrand is a product of two distinct types of functions.; One part reduces nicely when differentiated.; The other part requires a u-substitution to find its antiderivative.