(Method 3) Integral of x/sqrt(1-x^2)

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✅ 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞 𝐭𝐨 𝐜𝐡𝐞𝐜𝐤 𝐭𝐡𝐞 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧
Derivative of -sqrt(1-x^2) =    • Derivative of -sqrt(1-x^2)  

🙈 𝐒𝐚𝐦𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥, 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐦𝐞𝐭𝐡𝐨𝐝𝐬
[Method 1] - Integral of x/sqrt(1-x^2) - [u=√(1-x^2)] -    • (Method 1) Integral of x/sqrt(1-x^2) (subs...  
[Method 2] - Integral of x/sqrt(1-x^2) - [u=1-x^2] -    • (Method 2) Integral of x/sqrt(1-x^2) (subs...  
[Method 3] - Integral of x/sqrt(1-x^2) - [x=sin(u)] -    • (Method 3) Integral of x/sqrt(1-x^2)  

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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: x=sin(u)
00:10 Differentiate in both sides
00:18 Substitute x and dx
00:46 Use the 1=sin^2(u)+cos^2(u) identity
01:25 Simplify expression
01:48 Integrate sin(u)
01:53 Undo substitution: u in terms of x
02:04 Use the cos(arcsin(x)) formula
02:26 Add integration constant +C
02:32 Final answer!
02:39 See more!

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