Integral of x^2/(4x^2+1)

Опубликовано: 28 Октябрь 2024
на канале: Integrals ForYou

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✍🏼 https://integralsforyou.com - Integral of x^2/(4x^2+1) - How to integrate it step by step using the substitution method!

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:12 Multiply numerator and denominator by 4
00:21 Add +1-1 on the numerator
00:26 Split integral
00:57 Simplify and rewrite expression
01:21 Substitution: u=2x
01:27 Differentiate in both sides
01:36 Substitute 2x and dx
02:00 Take 1/2 outside the integral
02:19 Integrate 1 and 1/(1+u^2)
02:34 Undo substitution: u in terms of x
02:46 Add integration constant +C
02:53 Final answer!

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