Solving Integrals with Trig Substitution - 1/(25-x^2)

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Homework Help Overview

The problem involves integrating the function 1/(25-x^2), which suggests a connection to techniques such as trigonometric substitution or partial fractions. The context is rooted in integral calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster questions whether trigonometric substitution is appropriate for this integral, noting the absence of a square root. Some participants suggest using partial fractions, with one clarifying the factorization of the expression 25-x^2.

Discussion Status

The discussion has seen various approaches being proposed, including trigonometric substitution and partial fractions. While some guidance has been offered, there is no explicit consensus on the best method to use, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants are navigating the integration techniques available for this specific form, with some uncertainty about the applicability of trigonometric substitution due to the structure of the integral.

Bryon
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Hi Everyone!
I just need some guidance on this problem. I seem to have trouble what integration technique I need to use on integrals of this type.


Homework Statement



integrate 1/(25-x^2)

Homework Equations



sqrt(a^2-u^2)
arcsin(u/a)

The Attempt at a Solution



Would I be able to use trig substitution for this type of integral? It almost fits with the arcsin but the square root is missing.
 
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Try partial fractions since 25-x^2 = (5-x)^2.
 
snipez90 said:
Try partial fractions since 25-x^2 = (5-x)^2.
Partial fractions is the easiest way to go, but 25 - x^2 = (5 - x)(5 + x), which is not equal to (5 - x)^2.
 
Ok, I believe I figured it out.

I used trig substitution

set x = 5sinx
dx/dθ = 5cosx -> dx = 5cosx dθ

I got this... int 1/(25-(5sinx)^2) 5cosx dθ which is easy to reduce.
 

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