Integral of 1/sqrt(-x^2+2x+3) (substitution)
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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Write -x^2+2x+3 as 4-(x-1)^2
01:06 Substitution: x-1 = 2sin(u)
01:18 Differentiate in both sides
01:25 4-(x-1)^2 in terms of "u"
02:12 Substitute 4-(x-1)^2 and dx
02:41 Simplify expression
03:02 Integrate 1du
03:05 Undo substitution: u in terms of x
03:34 Add integration constant +C
03:41 Final answer!
03:46 See more!
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