Integral of (2x+7)/(4+(1+x)^2) (substitution)
✍🏼 https://integralsforyou.com - Integral of (2x+7)/(4+(1+x)^2) - How to integrate it step by step using the substitution method!
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00:00 Write 7 as 2+5
00:17 Split into two integrals
00:49 Rewrite expression
02:03 Substitution: u=x^2+2x+5
02:20 Differentiate in both sides
02:27 Substitution: v=(1+x)/2
02:35 Differentiate in both sides
02:46 Substitute x^2+2x+5 and (2x+2)dx
03:01 Substitute (1+x)/2 and dx
03:24 Integrate 1/u
03:28 Simplify and integrate 1/(1+v^2)
03:42 Undo substitution: u in terms of x
03:51 Undo substitution: v in terms of x
04:01 Add integration constant +C
04:11 Final answer!
04:15 See more!
𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭𝐬
► Integration by parts: • 🧑🔧 Integration by parts
► Integration by substitution: • 🧑🔧 Integration by substitution
► Integration by trig substitution: • 🧑🔧 Integration by trig substitution
► Integration by Weierstrass substitution: • 🧑🔧 Integration by Weierstrass substitution
► Integration by partial fraction decomposition: • 🧑🔧 Integration by partial fraction decomp...
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► Integration by partial fraction decomposition 👉 https://integralsforyou.com/integrati...
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