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Rewrite the trigonometric expression $\frac{1}{\cos\left(x\right)^4}$ inside the integral
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$\int\sec\left(x\right)^4dx$
Learn how to solve differential calculus problems step by step online. Solve the trigonometric integral int(1/(cos(x)^4))dx. Rewrite the trigonometric expression \frac{1}{\cos\left(x\right)^4} inside the integral. 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).