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Simplify the integral $\int\sec\left(x\right)^4dx$ applying the reduction formula, $\displaystyle\int\sec(x)^{n}dx=\frac{\sin(x)\sec(x)^{n-1}}{n-1}+\frac{n-2}{n-1}\int\sec(x)^{n-2}dx$
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$\frac{\sin\left(x\right)\sec\left(x\right)^{3}}{4-1}+\frac{4-2}{4-1}\int\sec\left(x\right)^{2}dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sec(x)^4)dx. Simplify the integral \int\sec\left(x\right)^4dx applying the reduction formula, \displaystyle\int\sec(x)^{n}dx=\frac{\sin(x)\sec(x)^{n-1}}{n-1}+\frac{n-2}{n-1}\int\sec(x)^{n-2}dx. Simplify the expression inside the integral. The integral \frac{2}{3}\int\sec\left(x\right)^{2}dx results in: \frac{2}{3}\tan\left(x\right). Gather the results of all integrals.