# Evaluate Indefinite integral as an infinite series

• Apr 15th 2010, 08:26 PM
racewithferrari
Evaluate Indefinite integral as an infinite series
Evaluate Indefinite integral as an infinite series

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• Apr 15th 2010, 08:38 PM
Failure
Quote:

Originally Posted by racewithferrari
Evaluate Indefinite integral as an infinite series

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