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Consider the integralsec2xtan3xdx

(a) Solve this integral by using integration by substitution with u = tan x.

(b) Solve this integral another way, by using integration by substitution with u = sec x.

Short Answer

Expert verified

(a)tan4x4+C

(b)tan4x4+C

Step by step solution

01

Step 1. Given information

Integral issec2xtan3xdx

02

Part (a) Step 1. Explanation

Let u=tanx

sec2xtan3xdx=u3du=u44+C=tan4x4+C

03

Part (b) Step 1. Explanation

Let u=secx.

du=secxtanxdx

sec2xtan3xdx=uu2-1du=u3-udu=u44-u22+C=sec4x4-sec2x2+C=tan4x4+C

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