Integral of 1/(sin(x)+cos(x))

🍏 𝐀𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐚 𝐝𝐚𝐲 𝐤𝐞𝐞𝐩𝐬 𝐭𝐡𝐞 𝐝𝐨𝐜𝐭𝐨𝐫 𝐚𝐰𝐚𝐲   / integralsforyou   💥 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞𝐬 𝐅𝐨𝐫𝐘𝐨𝐮    / @derivativesforyou   ✍🏼 𝐖𝐞𝐛𝐬𝐢𝐭𝐞 https://integralsforyou.com 🔧 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! #integralsforyou #integrals #integration