How do you find #int sec^2x/(tan^2x  3tanx + 2) dx# using partial fractions?
Factor the denominator
Perform a usubstitution
Make the substitution into the integral
Now we want to do partial fraction decomposition on this
Equating coefficients
Solving this system you get
Our integral becomes
Rewrite
Integrating we get
Using properties of logarithms this can be rewritten as
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To find the integral of sec^2(x) / (tan^2(x)  3tan(x) + 2) dx using partial fractions, follow these steps:

Factor the denominator: tan^2(x)  3tan(x) + 2 = (tan(x)  1)(tan(x)  2).

Express the fraction as a sum of partial fractions: sec^2(x) / ((tan(x)  1)(tan(x)  2)) = A/(tan(x)  1) + B/(tan(x)  2).

Find the values of A and B by equating coefficients: A(tan(x)  2) + B(tan(x)  1) = sec^2(x).

Clear denominators and solve for A and B.

After finding A and B, integrate each term separately.

Finally, combine the integrals to obtain the result.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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