USM is a single, systematic framework that unifies trigonometric, hyperbolic, and complex-exponential substitutions into one coherent method. No more hunting through a dozen separate “recipes” for different radicals or inverse-trig integrals—you rewrite x + b as e^(±i α) (or e^θ), track sign/branch choices algorithmically, and reduce everything to a rational (“polynomish”) integral in a new variable.

Why USM shines for ∫ e^(arccos(x)) dx:
• Transforms e^(arccos(x)) into simple powers of t = e^(–i arccos(x))
• Eliminates the usual integration-by-parts slog
• Integrates term-by-term in one shot, then back-substitutes for a crisp final form

📄 Dive deeper! Check out my draft article “A Unified Substitution Method for Integration” for full proofs, more examples, and the USM’s broader scope (link in bio).

#UnifiedSubstitutionMethod #USM #Calculus #Integration #MathAnimation #Manim #MathHack #STEM #Education #InstaMath #LearnWithAnimation #MathLife #GarciaUSM #ReadTheDraft

Multiply ANY Number by 5 Instantly! 🔥

👉 Even number × 5 → Divide by 2, then add 0
✔ 28 × 5 → 28 ÷ 2 = 14 → Add 0 → 140

👉 Odd number × 5 → Subtract 1, divide by 2, then add 5
✔ 37 × 5 → (37 - 1) ÷ 2 = 18 → Add 5 → 185

🔥 Try 46 × 5 and COMMENT your answer below! ⬇️
#MathHack

Multiply ANY Number by 5 Instantly! 🔥

👉 Even number × 5 → Divide by 2, then add 0
✔ 28 × 5 → 28 ÷ 2 = 14 → Add 0 → 140

👉 Odd number × 5 → Subtract 1, divide by 2, then add 5
✔ 37 × 5 → (37 - 1) ÷ 2 = 18 → Add 5 → 185

🔥 Try 46 × 5 and COMMENT your answer below! ⬇️
#MathHack

Did everyone know this? Why didn't anyone tell me? Why didn't any of my math teachers?

#MathHack
#Calculations
#MyMathTeachersWereAllBad

If I was a textbook author, I would just state an unsolved problem, show two steps and then end with "the proof is left as an exercise for the reader."

I'm going to solve the whole world peace thing next.

#ImBadatChoosingHashtaga #mathhack