Evaluate the indefinite integral. (Use C for the constant of integration.)

Question

tan^-1(5x) / 1+25x² dx

Answer 1

Let u = Tan^-1(5x). Then, du = 5 / (1 + 25x²)dx. So, 1 / (1 + 25x²)dx = (1/5)du

Therefore, ∫[Tan^-1(5x) / (1 + 25x²)]dx = (1/5)∫udu = (1/10)u² + C = (1/10)(Tan^-1(5x))² + C