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

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In summary, integrating into a new research team or laboratory can be made easier by getting to know your team members, communicating openly and actively listening, and offering your own insights and contributions. When integrating into a different research field, it is important to read relevant literature, attend conferences or seminars, and collaborate with researchers in that field. Challenges may include adjusting to a new culture, learning new techniques, and communication barriers, but being patient, open-minded, and willing to learn can help overcome these challenges. To ensure a smooth integration process, it is important to communicate openly, participate in team activities, seek out learning opportunities, and be open to feedback and constructive criticism.
  • #1
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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  • #2
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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  • #3
If y = (1/3)t + C, then dy/dt = 1/3, which is clearly not even remotely close to the original integrand.
 
  • #4
omg! i knowwwwwwwwwwwwwwwwww! i did it. that was so stupid of me. thank you.
 

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2. What are some strategies for integrating into a new laboratory?

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