Question

Help Plsssss :3

Answer 1

\[\int\limits \frac{ x^2+1 }{ (x-10)(x-9)^2 }\]
\[\left( \frac{ A }{ (x-10) }+\frac{ B }{ (x-9) } + \frac{ C }{ (x-9)^2 }\right) (x-10)(x-9)^2\]
\[A(x-9)^2+B(x-10)(x-9)+C(x-10)\]
\[x=9 \rightarrow C=-82\]
\[x=10 \rightarrow A=101\]
How would I find B?

Answer 2

where is your RHS?

Answer 3

the third line should be
\[A(x-9)^2+B(x-10)(x-9)+C(x-10)=x^2+1\]

Answer 4

From it,
if x=9, you have -C = 81+1=82, so C =-82. Good for you.

Answer 5

if x=10, you have A= 101
good also

Answer 6

hmmmmmmmm

Answer 7

Now, just give x an arbitrary number. I pick x =0, replace all A, C in

Answer 8

\[A(x-9)^2+B(x-10)(x-9)+C(x-10)=x^2+1\\101(0-9)^2+B(0-10)(x-9)+(-82)(0-10) =0^2+1\]

Answer 9

oh, forgot replace x=0 after B
but you got the idea. Now, solve for B. dat sit

Answer 10

\[101(0-9)^2+B(0-10)(0-9)+(-82)(0-10)=1\]

Answer 11

what?

Answer 12

Got it! Thanks!