<p>my teacher gave a pop quiz on integrals, and she put 2 questions on there I couldn't figure out. One, she told us to take off (integral tanx dx), but the other is still there. Please help me out with this, because we finish in class tomorrow!</p>
<p>integral (tan x)[ln(cos x)]dx</p>
<p>Thanks very much!</p>
<p>bring up my post!</p>
<p>S(x) = integral of x</p>
<p>S(tan(x)*ln( | cos(x) | ) dx)</p>
<p>Let,
u = ln( | cos(x) | )
dv = tan(x)dx
du = -tan(x)
v = -ln( | cos(x) | )</p>
<p>S(u d(v)) = uv - S(v d(u))</p>
<p>S(u d(v)) = ln( | cos(x) | ) * -ln( | cos(x) | ) - S( -ln( | cos(x) | ) * -tan(x) * dx)</p>
<p>S(u d(v)) = -[ ln( | cos(x) | )]^2 - S(ln( | cos(x) | ) * tan(x) * dx)</p>
<p>2*S(u d(v)) = -[ ln( | cos(x) | )]^2</p>
<p>S(u d(v)) = (-[ ln( | cos(x) | )]^2 )/2</p>
<p>EDIT: Blah, I was doing it backwards</p>
<p>EDIT2: averagemathgeek, because I'm an idiot :P</p>
<p>Why not use the substitution u=ln[cos(x)]?</p>
<p>Edit: It appears the above poster already figured out the substitution I mentioned, sorry for my error.</p>
<p>Second Edit: It appears that I have no clue what is going on, sorry for my error.</p>
<p>b/c then you'd have to find the integral of tan x!</p>
<p>eh, you're supposed to do that without knowing the integral of tan(x)?</p>
<p>EDIT: netshark, averagemathgeek and I are saying the same thing (I think). However, I believe that we are both assuming that you guys have covered the integrals of all of the trig functions</p>
<p>thanks so much! my teacher never taught us that...i appreciate the help.</p>