Exercise
$\int_0^{\frac{\pi\:}{2}}\:\frac{1}{cos^3x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function 1/(cos(x)^3) from 0 to pi/2. Rewrite the trigonometric expression \frac{1}{\cos\left(x\right)^3} inside the integral. 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.
Integrate the function 1/(cos(x)^3) from 0 to pi/2
Final answer to the exercise
$\frac{1}{2}\cdot \left(\tan\left(\frac{\pi }{2}\right)\sec\left(\frac{\pi }{2}\right)-\tan\left(0\right)\sec\left(0\right)+\ln\left|\sec\left(\frac{\pi }{2}\right)+\tan\left(\frac{\pi }{2}\right)\right|\right)$