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cherrilyn
 5 years ago
evaluate the integral
cherrilyn
 5 years ago
evaluate the integral

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cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{?}^{?}(x ^{2} + 3x 44)dx/(x+3)(x+5)(3x2)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1partial fraction decomp it looks like; unless we can factor the top to cancel some bottoms

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x^2 +3x 44 = A(x+5)(3x2) ; x = 3 x^2 +3x 44 = B(x+3)(3x2) ; x = 5 x^2 +3x 44 = C(x+3)(x+5) ; x = 2/3

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0woohoo thats what I got. but now how do I find the actual values of the letters?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.144 = A(2)(11) 44/22=A A = 2  25 59 = B(2)(17) 34 = B(34) B = 1 x^2 +3x 44 = C(x+3)(x+5) ; x = 2/3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1when x = a number that zeros the other 2; use it and solve for that letter

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0but sometimes it leaves behind more than one variable

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x^2 +3x 44 = C(x+3)(x+5) ; x = 2/3 (2/3)^2 +3(2/3)  44 = C(2/3 +3)(2/3 +5)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1sometimes it does, but use it first to get some solids :) with linears on the bottom, its not a problem

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0okay. for the last equation I got 4/9  42 = c(2)(2/3 + 5)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1(4/9) +2  44 = C(11/3)(17/3) (4/9)  42 = C(11/3)(17/3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1374/9 = C(187/9) C = 374/189 reduce as wanted

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0wow how do you work so fast?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1i use my head and mess up alot lol

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0lol oh... do you think you can help me with another similar problem?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1perhaps; but let me get thru this one first :)

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0okay! thanks for all of your help :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1we did C correctly right? that monster fraction scares me into thinking I messed it up lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1i typoed the 187 into a 189 ;)

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0wait, in this problem.. there is no Dx+E?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1so our integral becomes: [S] 2/(x+3)  1/(x+5)  2/(3x2) dx

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1the bottom is already factored for us into linear forms; linear form dont need the Dx+E form

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1if we had an irreducible quadratic in the denom; then we would use the Dx+E form above it to aid us

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1nope; that is a multiple of a linear and still only needs a A B C single atop it

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0really? how would it look.. A/x1 + B/x1 + c/x1?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x^2 + 10 is irreducible quadratic; cant be factored to real linears

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A/(x1) + B/(x1)^2 + C/(x1)^3

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0ohh.. hmm . and that would be... Ax+B/x^2+10?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1our integral has become: 2ln(x+3)  ln(x+5) 2ln(3x2) +C

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0thats the final answer

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1thats the form we would use above it yes :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1we could probably turn this into one ln(yadayada)+C if we want, but this is good :)
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