Integration by substitution problem

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SUMMARY

The integral problem presented is ∫ (x+2)⁵⁰(x+1)dx, which can be solved using the substitution method. The suggested substitution is u = x + 2, which simplifies the integral significantly. The initial concern about the solution being too lengthy for manual calculation is unfounded, as the substitution leads to a manageable expression. This confirms that the integral can indeed be solved without errors in the problem statement.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with substitution methods in integration
  • Knowledge of polynomial functions
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Practice solving integrals using substitution techniques
  • Explore advanced integration methods, such as integration by parts
  • Learn about polynomial long division for complex integrals
  • Study the application of definite integrals in real-world problems
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Students studying calculus, mathematics educators, and anyone looking to improve their skills in solving integrals using substitution methods.

madmike159
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Homework Statement



Using a suitable substitution find the solution to:

∫ (x+2)50(x+1)dx


Homework Equations





The Attempt at a Solution



I can't find a solution to this using substitution. Wolfram alpha give an answer that is too long to be calculated by hand. Can anyone work out the solution, or is there a mistake in the question which means it can't be solved?
 
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[tex]Let\; u=x+2[/tex]
 
What do you get if you let u= x+ 2? That seems to me to be the obvious substitution. It is certainly not "too long to be calculated by hand".
 

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