Integral of ln(ax+b) (substitution + by parts)

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Integral of ln(ax+b) - How to integrate it step by step using the substitution method and integration by parts!

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: t=ax+b
00:07 Differentiate in both sides
00:16 Substitute ax+b and dx
00:27 Rewrite expression
00:34 Parts: Integral of u dv = uv - Integral of v du
00:44 Choose u and dv
00:51 Differentiate u to get du
00:59 Integrate dv to get v
01:03 Substitute u, v and du
01:22 Simplify and integrate 1 dt
01:43 Take out "t" as common factor
01:51 Undo substitution: t in terms of x
02:04 Add integration constant +C
02:13 Final answer!

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𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition

𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮

𝐃𝐨𝐧𝐚𝐭𝐞

#integralsforyou #integrationbysubstitution #integrationbyparts

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🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:

🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:

👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉

IntegralsForYou

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nhannhan

Learning : ln(ax+b) integral by int(udv) = uv - int(vdu)
Thank you!

shreyansh_albatross

Brother take some problems regarding application of integrals like area of curve calculations etc....

k.dharamsharma

Please help
Integral lower limit (1) upper limit (2) of ((x)-1) sqrt 2-(x) dx for Substitution

Mente-de-hierro

Hello sir I have a question for you.
Why you write x^2 if you can write x²

rkeduniverse

integration of dx/((1-x^3)^(1/2))
Can you please explain this

subhikshamoorthy

Bhaiya ji log function hota h 🙄
ax+b ko ap t assume nhi kr skte h

math ko babaseer mtt banaeye

x+1 ka integration hota h :-xlog(x+1)-x+log(x+1)

Or agr apke form k according a=1 or b=1 rakh de toh same. Ana chahe tha jo nhi aa rha h

Or apko jo result aya h uska differentiation kr k log(ax+b) nhi aa rha h🙄

ABHI..._

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