# p3 intergration!Watch

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#1
oh man, this sucks!

integral of sec(0.5x + 1)tan(0.5x+1)

thanx, this is the easier stuff, but just cant do it!
0
14 years ago
#2
∫ sec(0.5x + 1)tan(0.5x+1) dx
Rewrite it as:
∫ sin(0.5x+1)/cos^2(0.5x+1) dx
Use the sub:
u=cos(0.5x+1)
Then:
du=-0.5sin(0.5x+1) dx

This transforms the integral into:
-2 ∫ -0.5sin(0.5x+1)/cos^2(0.5x+1) dx = -2 ∫ 1/u² du = 2/u + C = 2/cos(0.5x+1) + C = 2sec(0.5x+1) + C
0
#3
thanx, it kinda makes sense.

just wondeing as i havent learnt a substitution method yet, is there a easier way?
0
14 years ago
#4
(Original post by Tazzie)
oh man, this sucks!

integral of sec(0.5x + 1)tan(0.5x+1)

thanx, this is the easier stuff, but just cant do it!
You're just reversing a standard differentiation really.
The differential of secx is secxtanx.
The differential of sec(0.5x + 1) = 0.5sec(0.5x+1)tan(0.5x+1).
Hence the differential of 2sec(0.5x+1) = sec(0.5x+1)tan(0.5x+1). So 2sec(0.5x+1) + C is the desired integral.
0
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