( x - 3 ) e^x ( x - 1 ) ^3 ,dx is equal to - Vidyadip

MCQ

$\int {\frac{{\left( {x - 3} \right){e^x}}}{{{{\left( {x - 1} \right)}^3}}}\,dx}$ is equal to

A
$\frac{{{e^x}}}{{\left( {x - 1} \right)}} + c$
✓
$\frac{{{e^x}}}{{{{\left( {x - 1} \right)}^2}}} + c$
C
$\frac{{{-e^x}}}{{{{\left( {x - 1} \right)}^2}}} + c$
D
$\frac{{{2e^x}}}{{{{\left( {x - 1} \right)}^3}}} + c$

✓

Answer

Correct option: B.

$\frac{{{e^x}}}{{{{\left( {x - 1} \right)}^2}}} + c$

b
$\int e^{x}\left\{\frac{(x-1)-2}{(x-1)^{3}}\right\} d x$

$=\int e^{x}\left\{\frac{1}{(x-1)^{2}}-\frac{2}{(x-1)^{3}}\right\} d x$

$=\mathrm{e}^{\mathrm{x}} \frac{1}{(\mathrm{x}-1)^{2}}+\mathrm{c}$

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