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Rewrite the integrand $\sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right)$ in expanded form
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$\int_{0}^{\frac{\pi}{4}}\left(2\tan\left(x\right)\sec\left(x\right)-5\sec\left(x\right)^2\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function sec(x)(2tan(x)-5sec(x)) from 0 to pi/4. Rewrite the integrand \sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right) in expanded form. Expand the integral \int_{0}^{\frac{\pi}{4}}\left(2\tan\left(x\right)\sec\left(x\right)-5\sec\left(x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{\frac{\pi}{4}}2\tan\left(x\right)\sec\left(x\right)dx results in: 0.828428. The integral \int_{0}^{\frac{\pi}{4}}-5\sec\left(x\right)^2dx results in: -5.