# How do you find the indefinite integral of #int (4/(3t^2)+7/(2t))dt#?

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To find the indefinite integral of ( \int \left(\frac{4}{3t^2} + \frac{7}{2t}\right) dt ), you can break it down into two separate integrals:

- ( \int \frac{4}{3t^2} dt )
- ( \int \frac{7}{2t} dt )

Then, integrate each term separately using the power rule for integration. The result will be:

- ( \int \frac{4}{3t^2} dt = -\frac{4}{3t} + C_1 )
- ( \int \frac{7}{2t} dt = 7\ln|t| + C_2 )

Combine both results, and add the arbitrary constants ( C_1 ) and ( C_2 ) to get the final indefinite integral:

( \int \left(\frac{4}{3t^2} + \frac{7}{2t}\right) dt = -\frac{4}{3t} + 7\ln|t| + 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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