Thread: Evaluate Indefinite integral as an infinite series

1. Evaluate Indefinite integral as an infinite series

Evaluate Indefinite integral as an infinite series

2. Originally Posted by racewithferrari
Evaluate Indefinite integral as an infinite series

$\int\frac{e^x-1}{x}\,dx = \int\frac{\sum_{k=0}^\infty\frac{x^k}{k!}-1}{x}\,dx=\int\sum_{k=1}^\infty\frac{x^{k-1}}{k!}\,dx= \sum_{k=1}^\infty\int \frac{x^{k-1}}{k!}=\sum_{k=1}^\infty \frac{x^k}{k\cdot k!}+C$