xtanlx2dx SolutionLet x tan substitutution dx sec2 Integra

Solution

Let x= tan --------> substitutution

dx = sec²

Integrand = ² tan sec² d

Integrating by parts, (integrating tan sec² and differentiaing ² )

we get integral = ² sec² /2 - tan - ln(sec )

Substituting back, we get integral = [(tan inverse x)² (1+ x²)]/2 - x tan inverse x - [ln(1 + x²)] /2