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Expand the integral $\int\left(\sec\left(x\right)^6-\sec\left(x\right)^4\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int\sec\left(x\right)^6dx+\int-\sec\left(x\right)^4dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sec(x)^6-sec(x)^4)dx. Expand the integral \int\left(\sec\left(x\right)^6-\sec\left(x\right)^4\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sec\left(x\right)^6dx results in: \frac{\tan\left(x\right)\sec\left(x\right)^{4}}{5}+\frac{4\tan\left(x\right)\sec\left(x\right)^{2}}{15}+\frac{8}{15}\tan\left(x\right). Gather the results of all integrals. The integral \int-\sec\left(x\right)^4dx results in: \frac{-\sin\left(x\right)\sec\left(x\right)^{3}}{3}-\frac{2}{3}\tan\left(x\right).