# How do you integrate #int (2x+1)/((x+3)(x-2)(x-3)) # using partial fractions?

First, focus on writing the fraction in terms of partial fractions:

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Sort by degree:

Giving the system:

Solving which gives:

Thus, we know that

Splitting up the integral and refactoring constants:

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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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- Using #int sec x dx = ln|sec x + tan x | + c# , find #int 1/ sqrt (2x^2 - 4) dx# using suitable trigonometric substitution?
- What is the integral of #10sin(x/5)#?

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