Integration substitution rule help

Click For Summary
SUMMARY

The forum discussion centers on the integration of the function ∫ x^(1/4) . (x^(5/4) +1)^6 using the substitution rule. The user correctly applied the substitution u = x^(5/4) + 1, leading to the integral resulting in (4/5) * (u^(7/7)) + C. Upon converting u back to x, the solution is confirmed as valid, demonstrating proper application of integration techniques.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with substitution methods in integration
  • Knowledge of polynomial functions and their properties
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study advanced integration techniques, including integration by parts
  • Explore the use of definite integrals and their applications
  • Learn about the Fundamental Theorem of Calculus
  • Practice more complex substitution problems in integral calculus
USEFUL FOR

Students and educators in calculus, particularly those focusing on integration techniques, as well as anyone seeking to strengthen their understanding of substitution methods in integral calculus.

p.mather
Messages
19
Reaction score
0

Homework Statement


∫ x^(1/4) . (x^(5/4) +1)^6

Homework Equations



I used substitution rule with u = x^(5/4) +1

The Attempt at a Solution



I got an answer of

4/5 . (u^7/7) +c would that be correct
 
Physics news on Phys.org


Convert u back to x and take the derivative. Is it correct?
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 28 ·
Replies
28
Views
3K
Replies
5
Views
1K
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
3
Views
2K