Integration by parts method is generally used to find the integral when the integrand is a product of two different types of functions or a single logarithmic function or a single inverse trigonometric function or a function which is not integrable directly.
If f(x) and g(x) are two differentiable functions then
d[f(x) g(x)]/dx = f′(x) g(x) + f(x) g′(x)
By definition of anti derivative
f(x) g(x) = ∫ f′(x) g(x) dx+ ∫ f(x) g′(x) dx
∫ f(x) g′(x) dx = f(x) g(x) − ∫ f′(x) g(x) dx
Let u = f(x) and v = g(x)
du = f′(x) dx and dv = g′(x) dx
∫ u dv = uv − ∫ v du
If integrand contains any non-integrable functions directly from the formula, like log x, tan−1 x etc., take these unintegrable functions as u and other as dv.
If the integrand contains both the integrable function, and one of these is xn (where n is a positive integer). Then take u = xn.