indefinite integrals

Question

(tan^-1(7x))/(1+49x^2) dx evaluate the indefinite integral

Answer 1

Let u = Tan^-1(7x). Then, du = [7 / (1 + 49x²)]dx. So, 1 / (1 + 49x²)dx = (1/7)du

So, the given integral can be rewritten as (1/7)∫ udu = (1/14)u² + C = (1/14)[Tan^-1x]² + C