# How do you integrate #1/(s+1)^2 # using partial fractions?

You don't use partial fraction, do substitution

which is

and subsitute back you have :

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To integrate ( \frac{1}{(s+1)^2} ) using partial fractions, you express ( \frac{1}{(s+1)^2} ) as ( \frac{A}{s+1} + \frac{B}{(s+1)^2} ). Then, solve for ( A ) and ( B ) by equating coefficients. The result will be ( \frac{A}{s+1} + \frac{B}{(s+1)^2} ), where ( A = 1 ) and ( B = -1 ). Thus, the integral becomes ( \int \frac{1}{(s+1)^2} , ds = \int \frac{1}{s+1} , ds - \int \frac{1}{(s+1)^2} , ds ), which equals ( -\frac{1}{s+1} + C ).

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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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