How do you find the indefinite integral of #int (12/x^4+8/x^5) dx#?
We can revert to positive exponents:
Thus,
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To find the indefinite integral of ( \int \left(\frac{12}{x^4} + \frac{8}{x^5}\right) , dx ), you can split it into two separate integrals:
- ( \int \frac{12}{x^4} , dx )
- ( \int \frac{8}{x^5} , dx )
For the first integral, use the power rule for integration:
[ \int \frac{12}{x^4} , dx = -\frac{12}{3x^3} + C = -\frac{4}{x^3} + C ]
For the second integral, also use the power rule for integration:
[ \int \frac{8
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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.
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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- How do you evaluate the definite integral #int (3x^2-2x+1)dx# from [1,5]?
- How do you find the integral of #sec(3x)sec(3x)#?

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