Evaluate the integrals. A) Integral of tan^2 x sec^4 x dx. B) Integral of tan^2 x sec x dx.


Evaluate the integrals.

A) {eq}\int \tan^2 x \sec^4 x \, \mathrm{d}x {/eq}

B) {eq}\int \tan^2 x \sec x \, \mathrm{d}x {/eq}


The reverse process of differentiation is integration. It can be related by using fundamental theorem of calculus. By using substitution method complex integral can be reduced to standard from.

Answer and Explanation:

{eq}\int \tan^{2}x\sec^{4}xdx\\ =\int \tan^{2}x(1+\tan^{2}x)\sec^{2}xdx\\ =\int t^{2}(1+t^{2})dt\\ =\frac{\tan^{3}x}{3}+\frac{\tan^{5}x}{5}+c\\ {/eq}

{eq}b)\int \left (\sec^{2}x-1 \right )\sec xdx\\ =\frac{\sec x \tan x}{2} -\frac{\ln |\sec x+\tan x|}{2} {/eq}

Learn more about this topic:

Using Integration By Parts

from Math 104: Calculus

Chapter 11 / Lesson 7

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