(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Integral ( cos(x)/(1+cos(x))^.5 dx)

2. Relevant equations

3. The attempt at a solution

Integral ( cos(x)/(1+cos(x))^.5 dx)

Square it

Integral ( cos(x)^2/(1+cos(x) dx)

Multiply by the Conjugate

Integral ( cos(x)^2/(1+cos(x) * (1 - cos(x))/(1 - cos(x)) dx)

Take the square root and then multiply by sin(x)/sin(x)

Integral ( cos(x)(1-cos(x))^.5/(sin(x) * sin(x)/sin(x) dx )

Convert sin(x)^2 in denom to 1-cos(x)^2 then use u-sub, u= cos(x) du=-sin(x)

Integral -( u(1-u)^.5/(1-u^2) du )

w substitution w= (1-u)^.5 u = 1-w^2 du = -2w

Integral (1-w^2)w^2/(1-(1-2w^2+w^4) dw)

Reduce down to

Integral 2((1-w^2)/(2-w^2) dw )

I have more done but am leaving to go out to dinner now. Will post more of my work later if needed. Thanks in advance.

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# Integration, trig with double substitution

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