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$\int\left(\sec\left(x\right)+\tan\left(x\right)\right)\left(\sec\left(x\right)-\tan\left(x\right)\right)dx$
Learn how to solve problems step by step online. Solve the equation y=(sec(x)+tan(x))(sec(x)-tan(x)). Find the integral. Rewrite the integrand \left(\sec\left(x\right)+\tan\left(x\right)\right)\left(\sec\left(x\right)-\tan\left(x\right)\right) in expanded form. Expand the integral \int\left(\sec\left(x\right)^2-\tan\left(x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\sec\left(x\right)^2dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution.