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


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}

Learn more about this topic:

Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1

Related to this Question

Explore our homework questions and answers library