Final Answer
$\frac{\tan\left(x\right)\sec\left(x\right)^{2}}{3}+\frac{2}{3}\tan\left(x\right)+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\sec\left(x\right)^2\sec\left(x\right)^2dx$
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$\int\sec\left(x\right)^2\sec\left(x\right)^2dx$
Learn how to solve problems step by step online. Integrate the function sec(x)^2sec(x)^2. Find the integral. When multiplying exponents with same base we can add the exponents. Simplify the integral \int\sec\left(x\right)^{4}dx 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.
Final Answer
$\frac{\tan\left(x\right)\sec\left(x\right)^{2}}{3}+\frac{2}{3}\tan\left(x\right)+C_0$