Question

Find the indefinite integral: Integral of 1/(9 + (x - 10)^2) dx.

Answer 1

When an integral would be made simpler if one of the terms were differentiated, we can use integration by parts. The formula for integration by parts is derived by integrating the product rule for differentiation, which is given by (uv)′=u′v+uv′(uv)′=u′v+uv′, to yield ∫udv=uv−∫vdu∫udv=uv−∫vdu.