- #1

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## Homework Statement

Evaluate the integral:

integral of dx / (4+x^2)^2

## Homework Equations

x = a tan x theta

a^2 + x^2 = a^2 sec^2 theta

## The Attempt at a Solution

x = 2 tan theta

dx = 2sec^2 theta

tan theta = x/2

integral of dx / (4+x^2)^2

= 1/8 integral (sec^2 theta / sec^4 theta) d theta

= 1/8 integral (cos^2 theta) dtheta

= 1/16 integral 1 + cos 2 theta d theta

= 1/16 [ theta + sin 2 theta / 2 ] + c

= 1/16 [ theta + sin theta cos theta ] + c

= 1/16 [ tan ^-1 x/2 + ??? ] + c

"???" is where I get lost.

Did I do the problem wrong? I was really confused when the book gave me a problem without a square root.