Final answer to the problem
$\frac{1}{2}\tan\left(x\right)\sec\left(x\right)+\frac{1}{2}\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|+C_0$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric integral int(sec(x)^3)dx. Rewrite \sec\left(x\right)^3 as the product of two secants. We can solve the integral \int\sec\left(x\right)^2\sec\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.
Final answer to the problem
$\frac{1}{2}\tan\left(x\right)\sec\left(x\right)+\frac{1}{2}\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|+C_0$
