Integral of 1/(sin(x)+cos(x))
Автор: Integrals ForYou
Загружено: 2025-01-26
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🍏 𝐀𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐚 𝐝𝐚𝐲 𝐤𝐞𝐞𝐩𝐬 𝐭𝐡𝐞 𝐝𝐨𝐜𝐭𝐨𝐫 𝐚𝐰𝐚𝐲
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🔧 𝐔𝐬𝐞𝐟𝐮𝐥 𝐯𝐢𝐝𝐞𝐨𝐬
t=tan(x/2): sin(x), cos(x) and dx values 👉 • t = tan(x/2) (Weierstrass substitution)
🎓 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭𝐬
• 🧑🔧 Integration by parts
• 🧑🔧 Integration by substitution
• 🧑🔧 Integration by trig substitution
• 🧑🔧 Integration by Weierstrass substitution
• 🧑🔧 Integration by partial fraction decomp...
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: t=tan(x/2)
00:13 Value of sin(x), cos(x) and dx
00:40 Substitute sin(x), cos(x) and dx
01:07 Simplify expression
01:26 Rewrite expression
01:53 Partial fraction decomposition for 1/(t^2-2t-1)
05:06 Equation system with A and B
05:28 Find the value of A
06:32 Find the value of B
06:47 Rewrite expression 1/(t^2-2t-1)
08:19 Integrate 1/(t-√2-1) and 1/(t+√2-1)
08:53 Undo substitution: t in terms of x
06:49 Simplify expression
09:26 Add integration constant +C
09:38 Final answer!
09:44 See more!
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