Primitive of Arctan x: Ideas & Solutions

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SUMMARY

The primitive (antiderivative) of arctan(x) can be calculated using two methods: substitution and integration by parts. For substitution, let u = arctan(x), while for integration by parts, apply the formula ∫u dv = uv - ∫v du, where dv = dx and u = arctan(x). Both methods yield the same result, confirming their effectiveness in solving the integral of arctan(x) dx.

PREREQUISITES
  • Understanding of integration techniques, specifically integration by parts.
  • Familiarity with the arctangent function and its properties.
  • Knowledge of substitution methods in calculus.
  • Basic proficiency in handling definite and indefinite integrals.
NEXT STEPS
  • Study the derivation of the integral of arctan(x) using substitution.
  • Practice integration by parts with various functions to solidify understanding.
  • Explore advanced integration techniques, such as trigonometric substitution.
  • Learn about the applications of arctan(x) in real-world problems and physics.
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Students and educators in calculus, mathematicians focusing on integration techniques, and anyone seeking to deepen their understanding of antiderivatives involving inverse trigonometric functions.

kidia
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Please any idea on this,find the primitive of arctan x
 
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Two ways: Make the substitution u=arctan x, or use integration by parts,

[tex]\int u \ dv = uv - \int v \ du[/tex]

where dv=dx, u=arctan x (they really work out in the same way anyways).
 
Yah now I understand it will be the intergral of arctanxdx. thanx.
 

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