What is the integral from 0 to 1 of 1/x sin(1/x) ?

The integral from 0 to 1 of 1/x sin(1/x) is -0.9460830704+pi/2

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integral from 0 to 1 of 1/x sin(1/x)

\int_{0}^{1} \frac{1}{x} sin (\frac{1}{x}) d x

- 0.9460830704 + \frac{π}{2}

Decimal Notation

0.62471 \dots

Solution steps

\int_{0}^{1} \frac{1}{x} sin (\frac{1}{x}) d x

Compute the indefinite integral:

\int \frac{1}{x} sin (\frac{1}{x}) d x = - Si (\frac{1}{x}) + C

Compute the boundaries:

\int_{0}^{1} \frac{1}{x} sin (\frac{1}{x}) d x = - 0.9460830704 - (- \frac{π}{2})

= - 0.9460830704 - (- \frac{π}{2})

Simplify

= - 0.9460830704 + \frac{π}{2}

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What is the integral from 0 to 1 of 1/x sin(1/x) ?
The integral from 0 to 1 of 1/x sin(1/x) is -0.9460830704+pi/2