- #1

Saitama

- 4,243

- 93

## Homework Statement

The value of [tex]\int_0^{1} (\prod_{r=1}^{n} (x+r))(\sum_{k=1}^{n} \frac{1}{x+k}) dx[/tex] equals:

a)n

b)n!

c)(n+1)!

d)n.n!

(Can someone tell me how to make bigger parentheses using latex?)

## Homework Equations

## The Attempt at a Solution

I know that the question becomes a lot easier if i put n=1 or 2 and then integrate. But i was wondering if there is any proper way to solve it. I can't go further after expanding the given expression.

[tex]\int_{0}^{1} (x+1)(x+2)......(x+n)(\frac{1}{x+1}+\frac{1}{x+2}+.....\frac{1}{x+n})dx[/tex]

which is equal to

[tex]\int_{0}^{1} \sum_{r=1}^n \frac{(x+n)!}{x+r}[/tex]

I am stuck now, i can't find any way further.

Any help is appreciated.