# How do I find the integral #intt^2/(t+4)dt# ?

Explanation :

Simplifying further,

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To find ( \int \frac{t^2}{t + 4} , dt ):

- Perform polynomial division or use the method of partial fractions to break down the integrand.
- Once you have the integrand in a suitable form, integrate each term separately.
- Check your work by differentiating the result to ensure it matches the original integrand.

Let's perform the steps:

- Perform polynomial division or partial fractions:

[ \frac{t^2}{t + 4} = t - \frac{4t}{t + 4} ]

- Integrate each term separately:

[ \int t , dt - \int \frac{4t}{t + 4} , dt ]

[ = \frac{t^2}{2} - 4 \int \frac{t}{t + 4} , dt ]

For the second integral, you can use substitution or a suitable method to integrate ( \frac{t}{t + 4} ).

- After integrating each term, you'll have your final result.

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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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