Integrating 2t^2/(1+t^2)^2 with Trig Substitution

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Homework Help Overview

The problem involves integrating the function 2t²/(1+t²)², with a mention of using trigonometric substitution as part of the approach.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods for integration, including trigonometric substitution and integration by parts. There is a mention of an attempted solution that is deemed incorrect, prompting further exploration of the integration technique.

Discussion Status

The discussion includes attempts to clarify the integration method, with one participant suggesting integration by parts as an alternative. There is an acknowledgment of a mistake in the attempted solution, leading to a realization from another participant.

Contextual Notes

Participants are navigating through the complexities of integration techniques and the implications of their choices, with some expressing frustration over errors in their calculations.

Litcyb
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Homework Statement



integrate 2t^(2)/(1+t^2)^(2)

Homework Equations



trig sub 1+tan^2(x)= sec^2(x)

The Attempt at a Solution


the attempted solution is attached.
 

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Your derivation is not correct and the method you follow is a bit complicated. Try integration by parts, ∫u'vdt=uv-∫uv'dt, with u'=2t/(1+t^2)^2 and v=t.

ehild
 
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If y = (1/3)t + C, then dy/dt = 1/3, which is clearly not even remotely close to the original integrand.
 
omg! i knowwwwwwwwwwwwwwwwww! i did it. that was so stupid of me. thank you.
 

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