How to Integrate 1 / (1 + ∛x) dx | Calculus 2 Tutorial

Can you solve this beautiful integral? At first glance, the cube root in the denominator makes this look incredibly intimidating. But with one clever algebraic substitution, the radical vanishes, leaving behind a classic fraction that yields to simple polynomial long division!

In this video, we break down the integral of 1 / (1 + ∛x) dx using a clean, step-by-step approach. No messy tricks, no over-complicated math—just pure, elegant calculus that makes a hard problem feel easy.

Whether you're prepping for a university exam, trying to ace your AP Calculus test, or just love beautiful math problems, this elegant walkthrough is for you!

💡 WHAT YOU WILL LEARN:
• How to choose the perfect substitution to eliminate radical roots (u-substitution)
• How to rewrite variables and differentials (dx) flawlessly
• The polynomial division trick to simplify rational functions
• Integrating term-by-term to reach the final, clean solution

🎓 TARGET CURRICULA & EXAMS:
• AP Calculus BC (Advanced Integration Techniques)
• College Calculus II / Calculus 2
• UK A-Levels Further Mathematics
• MIT Integration Bee & Putnam Exam Prep

TIMESTAMPS:
0:00 - The Intimidating Problem
0:45 - The Clever Substitution Trick
2:15 - Simplifying the Rational Function
4:00 - Term-by-Term Integration
5:30 - Back-Substitution & Final Answer

If you enjoyed this elegant solution, make sure to like, subscribe, and turn on notifications for more step-by-step calculus tutorials!

#SmoothIntegral
#Calculus
#Integrals
#LearnMath
#MathShorts

Integration by parts
https://www.youtube.com/playlist?list=PL6AvcD1nJfDdvwz1TfrDkdFZxbuOlhGhS
Trigonometric Integrals
https://www.youtube.com/playlist?list=PL6AvcD1nJfDfnnLykqRB32aTWk1kFUo2L
Integration by substitution
https://www.youtube.com/playlist?list=PL6AvcD1nJfDfJyZ1l8fD3nXLGVhmfoidR
integral exponential functions
https://www.youtube.com/playlist?list=PL6AvcD1nJfDfUgTm4uCAPkebLoLTe6dqY
definite integrals
https://www.youtube.com/playlist?list=PL6AvcD1nJfDe5BAKXJBt-5z-XcgEi7ing
integration by partial fractions
https://www.youtube.com/playlist?list=PL6AvcD1nJfDfkj4tZRwNJg4_AEH835_9M
Double Integration Examples and Solutions
https://www.youtube.com/playlist?list=PL6AvcD1nJfDcnWh1kKkwfjsTJFXe-Z-3t
Triple Integration Examples and Solutions
https://www.youtube.com/playlist?list=PL6AvcD1nJfDfda91UA1nDxBl6Z3Ia-RIN

Видео How to Integrate 1 / (1 + ∛x) dx | Calculus 2 Tutorial канала smooth integrals