1-calculate-0-1-ln-1-x-x-2-x-3-dx-2-then-find-the-value-of-0-1-ln-1-x-5-dx-3-find-the-value-of-n-1-1-n-5n-1-

Question Number 41854 by math khazana by abdo last updated on 14/Aug/18

1) c a l c u l a t e \int_{0}^{1} l n (1 + x + x^{2} + x^{3}) d x

2) t h e n f i n d t h e v a l u e o f \int_{0}^{1} l n (1 - x^{5}) d x

3) f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{1}{n (5 n + 1)} .