Final answer to the problem
$\frac{\tan\left(x\right)\sec\left(x\right)^{2}}{3}+\frac{2}{3}\tan\left(x\right)+C_0$
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Step-by-step Solution
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. 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. Apply the trigonometric identity: \sin\left(\theta \right)\sec\left(\theta \right)^n=\tan\left(\theta \right)\sec\left(\theta \right)^{\left(n-1\right)}, where n=3.
Final answer to the problem
$\frac{\tan\left(x\right)\sec\left(x\right)^{2}}{3}+\frac{2}{3}\tan\left(x\right)+C_0$
