Posted by Shayna on Wednesday, January 18, 2012 at 8:45pm.
prove that the integral of arcsec(x) is equal to xarcsec(x)  lnx+ sqrt((x^2)1)

Calculus  Steve, Thursday, January 19, 2012 at 4:48am
Let x = secθ
dx = secθtanθ dθ
θ = arcsec x
Int(arcsec(x) dx)
= Int(θ secθtanθ dθ)
now integrate by parts
u = θ
du = dθ
dv = secθtanθ dθ
v = secθ
Int(θ secθtanθ) = θsecθ  Int(secθ dθ)
To integrate secθ you have to resort to a trick:
secθ (secθ + tanθ)/(secθ + tanθ) dθ
now the top is sec^2θ + secθtanθ
let u = secθ + tanθ and we have
1/u du
so, Int(secθ dθ) is lnsecθ + tanθ
and we end up with
Int(θ secθtanθ) = θsecθ  lnsecInt(θ secθtanθ) = θsecθ  Int(secθ dθ) + tanInt(θ secθtanθ)
= θsecθ  Int(secθ dθ)
Now, what does all that equal in x's?
θ = arcsec(x)
secθ = x
tanθ = √(x^21)
and you have your answer.

Calculus  PS  Steve, Thursday, January 19, 2012 at 4:52am
copypaste error. That last complicated line should read:
Int(θ secθtanθ) = θsecθ  Int(secθ dθ)
= θsecθ  lnsecθ + tanθ
Answer This Question
Related Questions
 Calculus  Find the volume of the solid whose base is the region in the xyplane...
 Calculus  Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9...
 Calculus  Graph the curve and find its exact length. x = e^t + e^t, y = 5  2t...
 Math  Let A denote the portion of the curve y = sqrt(x) that is between the ...
 Calculus  Evaluate the indefinite integral: 8xx^2. I got this but I the ...
 CALCULUS 2!!! PLEASE HELP!!  I'm having trouble with this question on arc ...
 Calculus Help Please Urgent!!!  Prove that the integral on the interval [a,b] ...
 Calculus II  Evaluate using usubstitution: Integral of: 4x(tan(x^2))dx ...
 Calculus  Given the equation xy = 2, set up an integral to find the length of ...
 Calculus 2 (Differential Equation)  How would you solve the following problem ...
More Related Questions