MCQ
$\int\limits_0^1 {\left( {\prod\limits_{r = 1}^n {(x + r)} } \right)\left( {\sum\limits_{k = 1}^n {\frac{1}{{x + k}}} } \right)} dx$ =
- A$n$
- B$n$ $ !$
- C$(n + 1)$ $ !$
- ✓$n · n$ $ !$
$\operatorname{Let} \ln \left(\prod_{r=1}^{n}(x+r)\right)=t$
$\sum_{k=1}^{n} \ln (x+k)=t$
$\Rightarrow \sum_{k=1}^{n} \frac{1}{x+k} d x=d t$
$l=\int_{\ln (n !)}^{\ln (n+1) !} e^{t} d t=\left[e^{t}\right]_{\ln (n) !}^{\ln (n+1) !}$
$(n+1) !-n !=n \cdot n !$
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