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Integral of e^-x/(1+e^-x) (substitution)
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Integral of e^-x/(1+e^-x) - How to integrate it step by step using the substitution method!
👋 Follow @integralsforyou on Instagram for a daily integral 😉
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: u=1+e^-x
00:13 Differentiate in both sides
00:33 Substitute 1+e^-x and (e^-x)dx
00:48 Rewrite expression
00:53 Integrate 1/u
00:58 Undo substitution: u in terms of x
01:05 Add integration constant +C
01:13 Final answer!
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 #integrals #integrationbysubstitution
👋 Follow @integralsforyou on Instagram for a daily integral 😉
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: u=1+e^-x
00:13 Differentiate in both sides
00:33 Substitute 1+e^-x and (e^-x)dx
00:48 Rewrite expression
00:53 Integrate 1/u
00:58 Undo substitution: u in terms of x
01:05 Add integration constant +C
01:13 Final answer!
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 #integrals #integrationbysubstitution
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