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Integral of sqrt(1-x)/(x+sqrt(x)) (substitution + substitution)
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๐ถ ๐๐ญ๐๐ฉ๐ฌ
00:00 Rewrite expression
00:31 Substitution: u=sqrt(x)
00:37 Differentiate in both sides
00:43 Substitute sqrt(x), x and (1/2sqrt(x))dx
01:14 Substitution: u=sin(t)
01:24 Differentiate in both sides
01:32 Substitute u, u^2 and du
01:57 Apply 1=sin^2(t)+cos^2(t)
02:42 Simplify expression
03:01 Apply 1=sin^2(t)+cos^2(t)
03:19 Apply a^2-b^2 = (a+b)(a-b)
03:57 Simplify expression
04:15 Integrate 1 and sin(t)
04:28 Undo substitution: t in terms of u
04:52 Simplify expression
05:16 Undo substitution: u in terms of x
05:27 Add integration constant +C
05:37 Final answer!
05:41 See more!
๐ ๐๐ซ๐ ๐ฒ๐จ๐ฎ ๐ฅ๐จ๐จ๐ค๐ข๐ง๐ ๐๐จ๐ซ ๐ ๐ฉ๐๐ซ๐ญ๐ข๐๐ฎ๐ฅ๐๐ซ ๐ข๐ง๐ญ๐๐ ๐ซ๐๐ฅ? ๐ ๐ข๐ง๐ ๐ข๐ญ ๐ฐ๐ข๐ญ๐ก ๐ญ๐ก๐ ๐ข๐ง๐ญ๐๐ ๐ซ๐๐ฅ ๐ฌ๐๐๐ซ๐๐ก๐๐ซ:
๐ ๐๐๐ฏ๐ ๐ฒ๐จ๐ฎ ๐ฃ๐ฎ๐ฌ๐ญ ๐ฅ๐๐๐ซ๐ง๐๐ ๐๐ง ๐ข๐ง๐ญ๐๐ ๐ซ๐๐ญ๐ข๐จ๐ง ๐ฆ๐๐ญ๐ก๐จ๐? ๐ ๐ข๐ง๐ ๐๐๐ฌ๐ฒ, ๐ฆ๐๐๐ข๐ฎ๐ฆ ๐๐ง๐ ๐ก๐ข๐ ๐ก ๐ฅ๐๐ฏ๐๐ฅ ๐๐ฑ๐๐ฆ๐ฉ๐ฅ๐๐ฌ ๐ก๐๐ซ๐:
๐ ๐ ๐จ๐ฅ๐ฅ๐จ๐ฐ @๐ข๐ง๐ญ๐๐ ๐ซ๐๐ฅ๐ฌ๐๐จ๐ซ๐ฒ๐จ๐ฎ ๐๐จ๐ซ ๐ ๐๐๐ข๐ฅ๐ฒ ๐ข๐ง๐ญ๐๐ ๐ซ๐๐ฅ! ๐
๐ ๐จ๐ฅ๐ฅ๐จ๐ฐ ๐๐ง๐ญ๐๐ ๐ซ๐๐ฅ๐ฌ ๐ ๐จ๐ซ๐๐จ๐ฎ
๐โโ๏ธ ๐๐จ๐ง๐๐ญ๐:
#integralsforyou #integrals #integration
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