Mastering Integrals: How to Solve the Integral of x^4*tan^-1(x) with Ease

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  • Thread starter Thread starter DarrenLockyer
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SUMMARY

The integral of x^4 * tan^-1(x) can be effectively solved using integration by parts. The recommended approach involves setting u = tan^-1(x) and dv = x^4 dx, which simplifies the integration process. This method reduces the complexity of the integral by leveraging the derivative of the arctangent function and the power of x. By applying this technique, one can systematically solve the integral without getting stuck.

PREREQUISITES
  • Understanding of integration techniques, specifically integration by parts.
  • Familiarity with the arctangent function and its properties.
  • Knowledge of basic calculus concepts, including derivatives and integrals.
  • Ability to manipulate algebraic expressions involving powers of x.
NEXT STEPS
  • Practice integration by parts with various functions to gain proficiency.
  • Explore the properties and derivatives of the arctangent function.
  • Study advanced integration techniques, including substitution and partial fractions.
  • Review examples of integrals involving products of polynomial and transcendental functions.
USEFUL FOR

Students and educators in calculus, mathematicians seeking to enhance their integration skills, and anyone looking to master complex integral calculations.

DarrenLockyer
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Hey i was wondering if anyone knew how to do:
The integral of : x^4*tan^-1 dx??

Im rater stuck on how to do it. plez help
 
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DarrenLockyer said:
Hey i was wondering if anyone knew how to do:
The integral of : x^4*tan^-1 dx??

Im rater stuck on how to do it. plez help

How can you say you are stuck and not show any work at all? If you are stuck then you must have tried something! What have you tried and why didn't it work.

Have you tried integration by parts at all?

Normally, when I see a power of x times another function, say [itex]\int x^n f(x)dx[/itex] I think of u= xn, dv= f(x)dx so that integration by parts will reduce the power of x. Here, however, tan-1(x) looks difficult to integrate so try the other way around. If u= tan-1(x) and dv= x4dx, what do you get?
 

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