- #1
jaychay
- 58
- 0
I am really struck with this question.
Thank you in advance.
Can Integration by Parts Solve This Tricky Question?
- Context: MHB
- Thread starter jaychay
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- Integration Method
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SUMMARY
The discussion centers on solving a complex integration problem using integration by parts. The user proposes setting \( u = x^3 \) and \( dv = x^2\sqrt{x^3+1} \) as a method to tackle the integral. An alternative approach suggested involves using substitution with \( t = x^3 + 1 \). Both methods are valid and can lead to the solution of the integral in question.
PREREQUISITES- Understanding of integration techniques, specifically integration by parts.
- Familiarity with substitution methods in calculus.
- Knowledge of polynomial and radical functions.
- Basic proficiency in handling integrals involving algebraic expressions.
- Practice problems using integration by parts with polynomial functions.
- Explore substitution methods in calculus, focusing on complex integrals.
- Review examples of integrals involving radical expressions.
- Study the properties and applications of definite and indefinite integrals.
Students and educators in calculus, mathematicians seeking to enhance their integration skills, and anyone interested in advanced techniques for solving integrals.
I am really struck with this question.
Thank you in advance.
- #2
skeeter
- 1,103
- 1
Using integration by parts, I would let
$u = x^3$ and $dv=x^2\sqrt{x^3+1}$Alternatively, one could use the same setup for the method of substitution letting $t= x^3+1$
$u = x^3$ and $dv=x^2\sqrt{x^3+1}$Alternatively, one could use the same setup for the method of substitution letting $t= x^3+1$
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