Integration: Choosing U-Sub vs. Parts

  • Context: Undergrad 
  • Thread starter Thread starter COCoNuT
  • Start date Start date
  • Tags Tags
    Integration parts
Click For Summary
SUMMARY

In integration, determining whether to use u-substitution or integration by parts is often based on the structure of the integrand. The discussion emphasizes that there is no definitive rule; instead, practitioners should develop an intuition for recognizing which method to apply. A common strategy involves attempting u-substitution first and, if unsuccessful, resorting to integration by parts. Ultimately, familiarity with various integral forms enhances problem-solving efficiency.

PREREQUISITES
  • Understanding of u-substitution in calculus
  • Knowledge of integration by parts technique
  • Familiarity with integral forms and their derivatives
  • Basic calculus concepts and terminology
NEXT STEPS
  • Practice identifying integrals suitable for u-substitution
  • Study advanced integration techniques, including trigonometric integrals
  • Explore the use of definite integrals in real-world applications
  • Learn about integral transformations and their applications
USEFUL FOR

Students and educators in calculus, mathematicians, and anyone looking to enhance their integration skills and problem-solving strategies in calculus.

COCoNuT
Messages
35
Reaction score
0
when doing integration, how do you know if you should use u-du substitution or integration by parts if the problem doesn't state it?
 
Physics news on Phys.org
Hopefully, you'll learn to "see" what to use after a while. Otherwise, first trying substitution and then (if that doesn't work) integration by parts often works...
 
Your basic strategy is to cast the integral into a familiar form. Sometimes it's obvious that one part of the integrand is the derivative of another part and other times it's obvious that a transformation will cast the integrand into something familiar. Otherwise, most of us try one then the other to see whether it leads anywhere. And sometimes neither one works!

I.e. there is no one size that fits all - which is why your calculus classes attempt to fill up your toolchest with as many tools as possible!
 

Similar threads

Undergrad A question about variables of integration
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad Bernoulli Equation with weird integral
  • · Replies 1 ·
Replies
1
Views
2K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Solving 2D Heat Equation w/ FEM & Galerkin Method
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Inverting an Equation Containing Elliptic Integrals
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Where did this substitution technique go wrong?
  • · Replies 27 ·
Replies
27
Views
4K
Undergrad Integrating a product of exponential and trigonometric functions
  • · Replies 21 ·
Replies
21
Views
4K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Integration Using Trigonometric Substitution
  • · Replies 8 ·
Replies
8
Views
3K
High School Why don't we account for the constant in integration by parts?
  • · Replies 16 ·
Replies
16
Views
4K