integral of { \int (sec (x) - cot (x))^2 dx }

Question:

integral of

{eq}\int (sec (x) - cot (x))^2 dx {/eq}

Indefinite Integral

This question is from the indefinite integral because of the limits are not given so we add constant C after integrating this. This will be solved by using simple integration formula.

Answer and Explanation:

{eq}\Rightarrow \ I=\int(sec(x)-cot(x))^{2}dx\\ \Rightarrow \ I=\int(sec^{2}(x)+cot^{2}(x)-2sec(x)cot(x))\\ \Rightarrow \ I=\int\sec^{2}(x)dx+\int\cot^{2}(x)dx-2\int\sec(x)cot(x))dx\\ \Rightarrow \ I=tan(x)+\int(cosec^{2}(x)-1)dx-2\int{cosec}(x)dx\\ \Rightarrow \ I=tan(x)-cot(x)-x+2\ln|(cosec(x)+cot(x))|+C\\ {/eq}


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Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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