Question

integration of x tan^2x

Answer 1

very simple by using uv rule

Answer 2

$\int{} x \: . \: {tan}^{2} x \: dx\\ \\ \int{} x \: .( {sec}^{2} x - 1) \: dx\\ \\ \int{} x \: . \: {sec}^{2} x \: dx \: - \int{x \: dx} \\ \\ Using \: chain \: rule \: of \: integratio n \: , \\ \\ x \int{} {sec}^{2} x \: dx- \int{ \frac{d(x)}{dx} (\int{} {sec}^{2} x \: dx) \: dx} - \int{} x \: dx \\ \\ x \int{} {sec}^{2} x \: dx- \: \int{} tan \: x \: dx \: - \int{} x \: dx \\ \\ \\ \boxed {x \: tan \: x \: - log(sec \: x) \: - \frac{ {x}^{2} }{2} \: + \: C }$