Integration - Trig Substitutions (solve for Y)

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Homework Help Overview

The problem involves solving for y as a function of x using integration techniques, specifically focusing on trigonometric substitutions. The original poster presents a differential equation that includes a square root and a polynomial expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to simplify the equation but expresses uncertainty about their approach, particularly regarding the use of substitution. Some participants suggest that the integral should be simpler than initially perceived, while others point out issues with the clarity of the mathematical notation used.

Discussion Status

Participants are engaging in a back-and-forth discussion, with some offering encouragement and suggesting that the problem may not be as complex as it seems. There is a recognition of the challenges posed by the notation, but no consensus has been reached regarding the best approach to take.

Contextual Notes

There are indications of confusion stemming from the use of LaTeX formatting, which some participants find unclear. The original poster's self-doubt about their calculations and the overall simplicity of the problem are also noted.

MeanGreen07
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Homework Statement



Solve the problem for y as a function of x

a) [tex](x^2+1)^2 \frac{dy}{dx}=\sqrt{x^2+1}[/tex]

Homework Equations




The Attempt at a Solution


After some simplifying, I get here but get stuck:


Did I go the wrong route going for the U sub? Were my calculations wrong to begin with? Any help is greatly appreciated!
 
Last edited:
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You are on the right track. But the tex is hugely unclear. In the end the integral should have come out to be dtheta/sec(theta). And that's hugely easy.
 
Stop texing. Your integrand is 1/sec(t)^3 and the dx is sec(t)^2*dt.
 
Sorry guys. My texing was bad and it appears my question was too simple for these forums.
 
Hey, hey. Sorry. I wasn't criticizing you. I can't TeX for s**t either. I'm just saying the problem is easier than you think. You just didn't put the integrand together with the dx and get a simple solution.
 
Dick said:
Hey, hey. Sorry. I wasn't criticizing you. I can't TeX for s**t either. I'm just saying the problem is easier than you think. You just didn't put the integrand together with the dx and get a simple solution.

Well, I feel somewhat better. LOL!

Thanks for the help!
 

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