Integration by Parts is a mathematical method used to evaluate integrals that involve products of functions. It allows us to transform a complex integral into a simpler one that can be easily solved.
You can use Integration by Parts when you have an integral that involves a product of two functions, and you are unable to directly evaluate it using other methods such as substitution or trigonometric identities.
The formula for Integration by Parts is ∫udv = uv - ∫vdu, where u and v are the two functions being multiplied together, and du and dv are their respective differentials.
When using the Integration by Parts formula, you should choose u and dv in a way that simplifies the integral on the right side of the equation. A general rule is to choose u as the part of the integrand that becomes simpler when differentiated, and dv as the part that becomes simpler when integrated.
If you get stuck on one part of the Integration by Parts process, you can try using other integration techniques like substitution or partial fractions. You can also try manipulating the integrand algebraically to make it easier to integrate. If you are still unable to solve the integral, it may be helpful to consult a calculus textbook or seek assistance from a math tutor or professor.