No label defined (Q1146)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | No label defined |
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Statements
B.26
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q_205
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\int_0^\infty\frac{|\sin(x)|}x~\mathrm dx&=\sum_{n=0}^\infty\int_{n\pi}^{(n+1)\pi}\frac{|\sin(x)|}x~\mathrm dx\\&=\sum_{n=0}^\infty\int_0^\pi\frac{\sin(x)}{x+n\pi}~\mathrm dx\\&=\sum_{n=0}^\infty\left[\frac1{(n+1)\pi}+\frac1{n\pi}-\int_0^\pi\frac{\cos(x)}{(x+n\pi)^2}~\mathrm dx\right]\tag{ibp}
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