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Solving integrals/ (1/x-sinx)dx

Integral of (1/x-sinx)dx dx

Limits of integration:

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The graph:

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The solution

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∫01(−sin⁡(x)+1x) dx\int\limits_{0}^{1} \left(- \sin{\left(x \right)} + \frac{1}{x}\right)\, dx 
Integral(1/x - sin(x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫(−sin⁡(x)) dx=−∫sin⁡(x) dx\int \left(- \sin{\left(x \right)}\right)\, dx = - \int \sin{\left(x \right)}\, dx

      1. The integral of sine is negative cosine:

        ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

      So, the result is: cos⁡(x)\cos{\left(x \right)}

    1. The integral of 1x\frac{1}{x} is log⁡(x)\log{\left(x \right)}.

    The result is: log⁡(x)+cos⁡(x)\log{\left(x \right)} + \cos{\left(x \right)}

  2. Add the constant of integration:

    log⁡(x)+cos⁡(x)+constant\log{\left(x \right)} + \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

log⁡(x)+cos⁡(x)+constant\log{\left(x \right)} + \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(−sin⁡(x)+1x) dx=C+log⁡(x)+cos⁡(x)\int \left(- \sin{\left(x \right)} + \frac{1}{x}\right)\, dx = C + \log{\left(x \right)} + \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
43.630748439861
43.630748439861

    Use the examples entering the upper and lower limits of integration.

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