(Method 3) Integral of 1/(1+e^x) (substitution)

Опубликовано: 11 Март 2026
на канале: Integrals ForYou

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

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🙈 𝐒𝐚𝐦𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥, 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐦𝐞𝐭𝐡𝐨𝐝𝐬
[Method 1] - Integral of 1/(e^x+1) - [Direct: +e^x-e^x] -    • (Method 1) Integral of 1/(e^x+1)
[Method 2] - Integral of 1/(e^x+1) - [u=e^x] -    • (Method 2) Integral of 1/(e^x+1) (substitu...
[Method 3] - Integral of 1/(e^x+1) - [u=1+e^-x] -    • (Method 3) Integral of 1/(1+e^x) (substitu...

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Multiply by e^-x/e^-x
00:13 Rewrite expression
00:24 Substitution: u=e^-x
00:30 Differentiate in both sides
00:42 Substitute e^-x + 1 and (e^-x)dx
00:55 Rewrite expression
01:01 Integrate 1/u
01:06 Undo substitution: u in terms of x
01:13 Add integration constant +C
01:19 Final answer!
01:23 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 parts 👉 https://integralsforyou.com/integrati...
► Integration by substitution 👉 https://integralsforyou.com/integrati...
► Integration by trig substitution 👉 https://integralsforyou.com/integrati...
► Integration by Weierstrass substitution 👉 https://integralsforyou.com/integrati...
► Integration by partial fraction decomposition 👉 https://integralsforyou.com/integrati...

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