New close form approximations of $łn{(1+x)}$

Sanjay Kumar Khattri

Based on Newton-Cotes and Gaussian quadrature rules, we develop several closed form approximations to $\ln{(1+x)}$. We also compare our formulae to the Taylor series expansion. Another objective of our work is to inspire students to formulate other better approximations by using the presented approach. Because of the level of mathematics, the presented work is easily embraceable in an undergraduate class.