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anonymous
 one year ago
Calculate the following integral.
anonymous
 one year ago
Calculate the following integral.

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2well we could do partial fractions again

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[x^41=(x^21)(x^2+1)=(x1)(x+1)(x^2+1)\] there is only 3 factors to worry about on the denominator

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so it won't be too terrible

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{x^32}{x^41}=\frac{A}{x1}+\frac{B}{x+1}+\frac{Cx+D}{x^2+1} \\ x^32=A(x+1)(x^2+1)+B(x1)(x^2+1)+(Cx+D)(x1)(x+1)\] so multiply out and reorder then compare both sides

freckles
 one year ago
Best ResponseYou've already chosen the best response.2Do you want to try to find A,B,C, and D ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got (A+B+C)X^3 + (AB)x^2 + (A+BC+D)x +(ABD) = x^3−2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(A+B+C)=1 A+B=0 (A+BC+D)=0 (ABD)=2

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.0you are working too hard

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:\ I only know how to expand and regroup

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[A(x^3+x^2+x+1)+B(x^3x^2+x1)+C(x^3x)+D(x^21)=x^32 \\ x^3(A+B+C)+x^2(AB+D)+x(A+BC)+(ABD)=x^32 \\ A+B+C=1 \\ AB+D=0 \\ A+BC=0 \\ ABD=2\]

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{x^32}{x^41}=\frac{A}{x1}+\frac{B}{x+1}+\frac{Cx+D}{x^2+1} \\ x^32=A(x+1)(x^2+1)+B(x1)(x^2+1)+(Cx+D)(x1)(x+1)\] let x=1

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.0\[1^32=A(1+1)(1^2+1)+B(11)(1^2+1)+(C1+D)(11)(1+1)\] \[12=A(1+1)(1+1)\] A=1/4

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.0let x=1 and you can get B let x=0 you can get d let x=i and you can get C

freckles
 one year ago
Best ResponseYou've already chosen the best response.2if you were having trouble solving the system, this may help I would add the first two equations together and the second two equations together: giving you: \[2A+(C+D)=1 \\ 2A(C+D)=2 \\ \text{ solving for } A \text{ by adding these two equations together } \\ 4A=1 \\ A=\frac{1}{4} \\ \text{ now see the equations that just have } A,B,C \text{ we can solve for } B \text{ and } C \text{ now } \\ A+B+C=1 \\ A+BC=0 \\ \text{ so } A=\frac{1}{4} \\ \frac{1}{4}+B+C=1 \\ \frac{1}{4}+BC=0 \text{ adding equations together } \\ \frac{2}{4}+2B=1 \\ 2B=\frac{3}{2} \\ B=\frac{3}{4} \\ \text{ then find } C \text{ using this system } \\ \text{ then you can finally find } D\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got the integral! thank you!
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