Tagged Questions

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Help with integration using partial fractions

I'm not sure how to get the values for $A$ and $B$ for the expression $$\frac{3}{x^2 - 16}.$$ I've split the expression into $$\frac{A}{x - 4} + \frac{B}{x + 4}.$$ I don't know what to do ...
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How to integrate $\int{\frac{6x}{x^3+8}dx}$

I'm having some trouble solving this integral using partial fraction method: $$\int{\frac{6x}{x^3+8}dx}.$$ After expanding $x^3+8$ into $(x-2)(x^2+2x+4)$ and expanding the original integral into ...
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Integral of rational functions.

I want to evaluate this integral: $$\int{\frac{ax+b}{(x^2+2px+q)^n}}dx$$ The book only says to integrate by parts $\int{\dfrac{1}{(x^2+2px+q)^{n-1}}dx}$, for simplicity if $n = 2$ I get: ...
Integral of $\int \frac{x^2 - 5x + 16}{(2x+1)(x-2)^2}dx$
I am trying to find the integral of this by using integration of rational functions by partial fractions. $$\int \frac{x^2 - 5x + 16}{(2x+1)(x-2)^2}dx$$ I am not really sure how to start this but ...
The given problem is $\int{x\over x^3-1}dx$. I know this equals $${1\over3}\int {1\over x-1}-{x-1\over x^2+x+1}dx,$$ which can be separated into {1\over3}\int {1\over x-1}dx - ...