Solving Bizarre Integral: x/[z2(x2+z2)1/2]

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SUMMARY

The integral discussed is 1/[(x²+z²)³/2] with respect to x, which appears in electromagnetism examples. The textbook solution is x/[z²(x²+z²)¹/2]. The initial approach taken was -1/(x(x²+z²)¹/2), which is incorrect. A suggested substitution for solving the integral is x=z tan(u), which simplifies the process and addresses the constant left out in the original attempt.

PREREQUISITES
  • Understanding of integral calculus, specifically techniques for solving definite and indefinite integrals.
  • Familiarity with trigonometric substitutions in integration, particularly x = z tan(u).
  • Knowledge of electromagnetism concepts where such integrals commonly arise.
  • Ability to manipulate algebraic expressions involving square roots and powers.
NEXT STEPS
  • Study the method of trigonometric substitution in integrals, focusing on examples similar to x=z tan(u).
  • Review integral calculus textbooks that cover advanced techniques for solving complex integrals.
  • Explore applications of integrals in electromagnetism to understand their practical significance.
  • Practice solving integrals involving square roots and powers to improve proficiency.
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Students and professionals in physics and engineering, particularly those working with electromagnetism and integral calculus, will benefit from this discussion.

Bigfoots mum
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Now then, I am close to shedding a tear with this one.

This integral has been popping up in a few electromag examples iv been doing and i have absolutely no idea what's going on here.

The integral is 1/[(x2+z2)3/2] with respect to x

According to the textbook the answer is x/[z2(x2+z2)1/2]

I initially, without evening really thinking, went straight for -1/(x[x2+z2]1/2)

Any ideas?
Thanks
 
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Use the substitution [itex]x=z \tan u[/itex].
 
btw, you left a constant
 

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