MCQ
The value of $\int {\frac{1}{{{{(x - 5)}^2}}}\,\,dx} $ is
- A$\frac{1}{{x - 5}} + c$
- ✓$ - \frac{1}{{x - 5}} + c$
- C$\frac{2}{{{{\left( {x - 5} \right)}^3}}} + c$
- D$ - 2{\left( {x - 5} \right)^3} + c$
✓
Answer
Correct option: B.
$ - \frac{1}{{x - 5}} + c$
b
(b)$I = \int {\frac{1}{{{{(x - 5)}^2}}}dx} $$ = \frac{{{{(x - 5)}^{ - 2 + 1}}}}{{ - 2 + 1}} + c = \frac{{{{(x - 5)}^{ - 1}}}}{{ - 1}} + c$
$ = - \frac{1}{{(x - 5)}} + c$.
(b)$I = \int {\frac{1}{{{{(x - 5)}^2}}}dx} $$ = \frac{{{{(x - 5)}^{ - 2 + 1}}}}{{ - 2 + 1}} + c = \frac{{{{(x - 5)}^{ - 1}}}}{{ - 1}} + c$
$ = - \frac{1}{{(x - 5)}} + c$.
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