The Integration by Parts Calculator helps integrate products of functions by applying the integration-by-parts identity derived from the product rule.
Formula
The standard formula is ∫u dv = uv − ∫v du. A good choice of u usually makes du simpler, while dv is selected because it can be integrated easily.
Worked example
For ∫x eˣ dx, choose u = x and dv = eˣ dx. Then du = dx and v = eˣ. Therefore, ∫x eˣ dx = xeˣ − ∫eˣ dx = eˣ(x − 1) + C.
When to use it
Integration by parts is especially useful for products involving polynomials, logarithms, inverse trigonometric functions, or exponentials. For repeated products, the method may need to be applied more than once.