Integral (maybe simple maybe hard)

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SUMMARY

The integral of (t^2) / (1+2t) can be solved using the substitution method with u = 1 + 2t. Wolfram Alpha provides the correct solution, which can be verified through proper application of this substitution. The discussion highlights that integration by parts is not effective for this problem, and suggests that long division of the integrand may simplify the process. Participants emphasize the importance of showing work to identify errors in the substitution method.

PREREQUISITES
  • Understanding of basic integration techniques, including substitution and integration by parts.
  • Familiarity with polynomial long division for simplifying rational functions.
  • Knowledge of the function properties and behavior of rational expressions.
  • Experience using computational tools like Wolfram Alpha for verification of solutions.
NEXT STEPS
  • Practice integration using u-substitution with various rational functions.
  • Learn polynomial long division techniques to simplify complex integrands.
  • Explore advanced integration techniques, including partial fraction decomposition.
  • Utilize Wolfram Alpha to check solutions for different types of integrals.
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone seeking to improve their problem-solving skills in integral calculus.

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Homework Statement


integrate (t^2) / (1+2t) . Wolfram alpha gave this as the answer: http://www4a.wolframalpha.com/Calculate/MSP/MSP957620di145hih25dggd00002hc5g230hb2h25hd?MSPStoreType=image/gif&s=24&w=229.&h=36.

The Attempt at a Solution



I tried a u-substitution and couldn't arrive at a solution. Any other suggestions! Int by parts doesn't seem to work either!
 
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The only easy method that comes to mind for me is to split the integrand into easier parts by long division.
 
hello.world said:

Homework Statement


integrate (t^2) / (1+2t) . Wolfram alpha gave this as the answer: http://www4a.wolframalpha.com/Calculate/MSP/MSP957620di145hih25dggd00002hc5g230hb2h25hd?MSPStoreType=image/gif&s=24&w=229.&h=36.

The Attempt at a Solution



I tried a u-substitution and couldn't arrive at a solution. Any other suggestions! Int by parts doesn't seem to work either!
The substitution u = 1+2t should work. I'm guessing that's what you tried, but you messed up somewhere along the way. Show your work.
 
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