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## Homework Statement

∫ dx/ x

^{2}(√4-x

^{2})

## Homework Equations

x=2sinθ

dx=2cosθdx

sin

^{2}θ= (1 + cos (2θ))/2

## The Attempt at a Solution

First attempt:

Plug in the trig sub and get:

∫2cosθdθ/4sin

^{2}θ2cosθ

The two cos θ cancel leaving

∫ dθ/ (4sin

^{2}θ)

Now I replace the sin

^{2}θ with (1-cos2θ)/2

and get

1/2 ∫dθ/(1-cos2θ)

I use u sub with the cos2θ

u=2θ

du/2=dθ

∫cosudu= sin2θ/2

I plug it back into the original equation

1/2 [ 2/θ-sin2θ]= 1/(θ-2sinθcosθ)

I retrieve the x from the original equation to get

4/ arcsin(x/2) -(x)(√(4-x

^{2}))

I may be doing something completely wrong, but I can't figure out where. Any hint on where to find the mistake? I keep practicing trig sub problems and I can not get any right. It might have to do with the derivation of the equations, but I am not sure.

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