Integral of sqrt(cos(x)/sin^5(x)) (substitution)
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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Write cos(x)/sin^5(x) as (cos(x)/sin(x))*(1/sin^4(x))
00:18 Use the √(ab) = √a * √b property
00:38 Write cos(x)/sin(x) as cot(x) and simplify √1/sin^4(x)
00:54 Substitution: u = cot(x)
01:03 Differentiate in both sides
01:21 Substitute cot(x) and dx
01:33 Rewrite expression
01:39 Integrate u^(1/2)
01:46 Rewrite expression
01:54 Undo substitution: u in terms of x
02:06 Add integration constant +C
02:12 Final answer!
02:17 See more!
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