19/12/2025
https://www.facebook.com/share/p/1AAwMPpFdK/
∫(x+1)/[x(1+xe^x)] dx = ???
Description:
⚡ Complex Looking but Simple Result!
∫(x+1)/[x(1+xe^x)] dx = ???
Beautiful simplification! 🎯
→ Rewrite: (x+1)/(x+x²e^x)
→ Simplify: (1 + 1/x)/(1+xe^x)
→ Spot pattern: d/dx[1+xe^x] = e^x+xe^x
→ This connects to our numerator!
→ Let u = 1+xe^x
→ Integrate: ∫du/u = ln|u| + C
→ Answer: ln|1+xe^x| + C ✓
Simple, elegant, brilliant! 💡
Hidden logarithm patterns are everywhere! 🔥
