Learn how to solve problems step by step online. Solve the trigonometric integral int(cos(x)/(sec(x)^5))dx. Simplify \frac{\cos\left(x\right)}{\sec\left(x\right)^5} into \cos\left(x\right)^{6} by applying trigonometric identities. Apply the formula: \int\cos\left(\theta \right)^ndx=\frac{\cos\left(\theta \right)^{\left(n-1\right)}\sin\left(\theta \right)}{n}+\frac{n-1}{n}\int\cos\left(\theta \right)^{\left(n-2\right)}dx, where n=6. The integral \frac{5}{6}\int\cos\left(x\right)^{4}dx results in: \frac{5\cos\left(x\right)^{3}\sin\left(x\right)}{24}+\frac{5}{8}\left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right). Gather the results of all integrals.

Solve the trigonometric integral int(cos(x)/(sec(x)^5))dx