# How do you find the indefinite integral of #int (5x^2 – 4x + 7)/((x^2+1)(2x – 1)) dx#?

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To find the indefinite integral of (\int \frac{5x^2 - 4x + 7}{(x^2 + 1)(2x - 1)} dx), you can use partial fraction decomposition followed by standard integration techniques. After decomposing the rational function into partial fractions, you can integrate each term separately.

Here are the steps:

- Decompose the rational function (\frac{5x^2 - 4x + 7}{(x^2 + 1)(2x - 1)}) into partial fractions.
- Once decomposed, integrate each term separately.
- Combine the integrals of the partial fractions to find the indefinite integral of the original function.

The decomposition and integration steps might involve algebraic manipulation and substitution techniques. Once integrated, you should have the indefinite integral of the given function.

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To find the indefinite integral of (\int \frac{{5x^2 - 4x + 7}}{{(x^2+1)(2x - 1)}} , dx), you can use partial fraction decomposition to split the fraction into simpler fractions. After that, you can integrate each term separately. Once integrated, you can combine the results to find the overall indefinite integral.

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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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