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$\int\left(\sec\left(x\right)^2-1\right)\cos\left(x\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of (sec(x)^2-1)cos(x). Find the integral. Rewrite the integrand \left(\sec\left(x\right)^2-1\right)\cos\left(x\right) in expanded form. Expand the integral \int\left(\sec\left(x\right)^2\cos\left(x\right)-\cos\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Apply the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right)^n=\sec\left(\theta \right)^{\left(n-1\right)}, where n=2.