Oops, typo, my bad.tomwilliam2 said:I wasn't getting where the sqrt cam from in the first response
Integration by parts is a method used in calculus to solve integrals that involve products of functions. It is based on the product rule for differentiation, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function.
Integration by parts is used when the integral involves a product of functions that cannot be easily solved using other methods such as substitution or trigonometric identities. It is especially useful for integrals involving logarithmic, exponential, or polynomial functions.
To solve an integral using integration by parts, you must first identify which function can be differentiated and which function can be integrated. Then, you can use the formula: ∫ u dv = uv - ∫ v du, where u is the function that can be differentiated and dv is the function that can be integrated. You will then continue to integrate the remaining integral until it can be solved, or until the integral repeats itself.
Yes, integration by parts can be used for both indefinite and definite integrals. When solving a definite integral using integration by parts, you will need to evaluate the limits of integration and substitute them into the final solution.
One helpful tip for making integration by parts easier is to choose u and dv in a way that will make the resulting integral simpler to solve. This can involve choosing u to be the most complicated function in the integral or choosing dv to be a function that becomes simpler when differentiated.