Find the integral {eq}\int\frac{dx}{\cos^2x \sqrt{1+ \tan x}} {/eq}.

Question:

Find the integral {eq}\int\frac{dx}{\cos^2x \sqrt{1+ \tan x}} {/eq}.

Solving an Indefinite Integral Using u-Substitution


The question presents an indefinite integral. Using the famous u-substitution technique, we find an antiderivative of the integrand. The integrand function contains trigonometric functions and we use the u-substitution method to help us obtain an antiderivative. The u-substitution method can also be used to evaluate definite integrals quite effectively while changing the two limits of integration in the process.


Answer and Explanation:

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Given the indefinite integral

{eq}\displaystyle \int \frac {dx}{\cos^2 x \; \sqrt {1+\tan x}} = \int \frac {\sec^2 x \; dx}{\sqrt{1+\tan x}}...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


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