how do u solve the integral xsecxtanx????

4 Answers

• We could let u = x, dv = secx tanx dx

  du = dx, v = sec x

  We get

  x*secx – ∫ secx dx

  = x*secx – ln|sec x + tan x| + C

• by parts

  ∫uv’ dx= uv – ∫vu’ dx

  so if

  u = x

  v’ = secxtanx

  u’ = 1

  v = secx

  ∫xsecxtanx dx = xsecx – ∫secx dx

  ∫secx = ln |secx + tanx| + C

  So:

  ∫xsecxtanx dx = xsecx – ln |secx + tanx| + C

• dv = secx tanx dx

  u = x

  du = dx

  v= secx

  uv – integral v du

  x secx – integral secx dx

• Integrate by parts.

  Let u = x, dv = sec x * tan x dx

  Then du = dx and v = sec x + C (but you let C = 0 without loss of generality, so v = sec x)

  Then int(x * sec x tan x dc)

  = int( u dv) = u * v – int(v du)

  = x * sec x – int(sec x dx)

  = x * sec x – ln |sec(x) + tan(x)| + C

  Hope this helps.