Integration by parts is a technique used in calculus to find the integral of a product of two functions. It involves breaking down the original function into two parts and using a specific formula to solve for the integral.
You should use integration by parts when the integral you are trying to solve contains a product of two functions, and the integral of one of those functions is easier to calculate after differentiating it.
The formula for integration by parts is ∫udv = uv - ∫vdu, where u and v are the two functions being integrated, and dv and du are their respective differentials.
Step 1: Identify the u and v functions in the integral.Step 2: Use the formula ∫udv = uv - ∫vdu to solve for the integral.Step 3: Differentiate the u function and integrate the v function.Step 4: Substitute the values back into the formula and simplify the integral.Step 5: Solve for the remaining integral using techniques such as substitution or integration by parts again if necessary.
Yes, the order is usually determined by the acronym "LIATE": Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential. The function that falls first in this order should be chosen as the u function.