# Integrate the following #int t/(t^4 +2) dt #?

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I solved this way:

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To integrate the function ( \int \frac{t}{t^4 + 2} , dt ), you can use the substitution method. Let ( u = t^2 ). Then ( du = 2t , dt ). Making the substitution, the integral becomes ( \frac{1}{2} \int \frac{1}{u^2 + 2} , du ). This integral can be solved by using the inverse tangent function, so the final result is ( \frac{1}{4} \tan^{-1} \left( \frac{t^2}{\sqrt{2}} \right) + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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