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$\int\cot\left(x\right)^2\left(\sec\left(x\right)^2-1\right)dx$
Learn how to solve differential calculus problems step by step online. Find the integral of cot(x)^2(sec(x)^2-1). Find the integral. Rewrite the integrand \cot\left(x\right)^2\left(\sec\left(x\right)^2-1\right) in expanded form. Expand the integral \int\left(\csc\left(x\right)^2-\cot\left(x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\csc\left(x\right)^2dx results in: -\cot\left(x\right).