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evaluate the intergral -1 to 6 (x-2)/(x^2-5x-14) dx

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\[\int\limits_{-1}^{6} \frac{ x-2 }{ x^2-5x-14 }\]
\[\int\limits_{-1}^{6} {x-2 \over (x+2)(x -7)} dx\] now do the whole partial fractions thing
\[\frac{ A }{ x-7 } + \frac{ B }{ x+2 }\] then getting everything with the same denominator I get.. \[x-2 = A(x+2) + B (x-7)\] then plugging in the different zeros, x=7 and x=-2 I solve for A and B. \[ A = \frac{ 5 }{ 9 }\] \[ B = \frac{ 4}{ 9 }\] Now the overall equation looks like: \[= \frac{ 5 }{ 9 } \int\limits_{}^{} \frac{ 1 }{ x-7 } dx + \frac{ 4 }{ 9 } \int\limits_{}^{} \frac{ 1 }{ x+2 } dx\] now what..? am I even doing this right?

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yes... but in this form now its put into the ln form....
you got it into the like ... i cant think of the name but its a form name.... but you did it right
right. so it would be \[= \left[ \frac{ 5\ln |x-7| }{ 9 } + \frac{ 4\ln |x+2| }{ 9 } \right] _{-1} ^{6}\] and then I evaluate it at x=6 and then subtract x=-1 ?
yeah. nice job.

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