# Tagged Questions

Rewriting rational function in the form of partial fractions is often useful when calculating integrals.

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### given an equation, find A and B

I can easily solve this problem by finding A and B, and then A+B. My question is where there is a way to obtain A+B without finding A and B first. The problem is supposed to be challenging, but it ...
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### Easy partial fraction decomposition with complex numbers

There is an easy method to perform a partial fraction decomposition - described here, under the "Repeated Real Roots" title, for the coefficient A2. The problem is ...
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Suppose we know $\int \frac{1-x^2}{(x^2+1)^2}=\frac{x}{x^2+1}+C$ How to compute $\int \frac{1}{(x^2+1)^2}dx$? I tried writing it as $\frac{1+x^2-x^2}{(x^2+1)^2}=\frac{1-x^2}{(x^2+1)^2}+\frac{x^2}{(x^... 3answers 62 views ### How do you use partial fraction decomposition to break up$1/(s+4)^2$? How do you use partial fraction decomposition to break up$1/(s+4)^2$? The usual method isn't giving me an answer. 1answer 20 views ### Question about partial fractions and the order of two linear factors I have a question on the topic of partial fraction and decomposition. Lets say I have the integral of$\frac{1}{(x^2 - x - 2)}$. When I want to find out the A and B values, I first have to get linear ... 1answer 35 views ### Use Laplace Transformations to solve$y''+2y'+5y=3e^{-x}sin(x)$, with$y(0)=0$,$y'(0)=3$I've gotten this far and I cannot proceed:$L[y]=\frac{L[3e^{-x}sin(x)]+3}{p^2+2p+5}= \frac{3}{((p+1)^2+1)(p^2+2p+5)}+\frac{3}{p^2+2p+5}$I'm finding it impossible to find the inverse to solve for$...
I have the following problem: $$\sum^{\infty}_{n=1}\dfrac{2}{\left(n+2\right)\sqrt{n}+n\sqrt{n+2}}$$ I should find the sum of this sequence. I tried to simplify but it does not work.