-x-5-x-22 d x-A- ln - x -1-7-x-2- C- ln - x -2-7- x -2- C- ln - x -2-7-2- x -1- CD- ln -x-1-7-x-1-C

The correct option is B ln|(x 2)| 7/(x 2)+CLet x+5/(x 2)^2 = A/x 2+B/(x 2)^2 =A(x 2)+B/(x 2)^2 A = 1 and B 2A = 5 B = 7 So, we'll have ∫1/(x 2)+7/(x 2)^2dx ...

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Byju's Answer

Standard XII

Mathematics

Special Integrals - 3

∫x+5/x-22 d x...

Question

$\int \frac{x + 5}{(x - 2)^{2}} d x$ = - .

ln | (x - 1) | - \frac{7}{(x - 2)} + C

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ln | (x - 2) | - \frac{7}{(x - 2)} + C

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ln | (x - 2) | - \frac{7}{(x - 1)} + C

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ln | (x - 1) | - \frac{7}{(x - 1)} + C

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Solution

The correct option is B $ln | (x - 2) | - \frac{7}{(x - 2)} + C$
Let $\frac{x + 5}{(x - 2)^{2}} = \frac{A}{x - 2} + \frac{B}{(x - 2)^{2}}$
$= \frac{A (x - 2) + B}{(x - 2)^{2}}$

A = 1 and B - 2A = 5
B = 7

So, we'll have

$\int \frac{1}{(x - 2)} + \frac{7}{(x - 2)^{2}} d x = ln | (x - 2) | - \frac{7}{(x - 2)} + C$

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∫x+5(x−2)2dx= - .

The correct option is B ln|(x−2)|−7(x−2)+CLet x+5(x−2)2=Ax−2+B(x−2)2 =A(x−2)+B(x−2)2 A = 1 and B - 2A = 5 B = 7 So, we'll have ∫1(x−2)+7(x−2)2dx=ln|(x−2)|−7(x−2)+C

$\int \frac{x + 5}{(x - 2)^{2}} d x$ = - .