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(x-csc(x)cot(x))
Solving integrals/ (x-csc(x)cot(x))

Integral of (x-csc(x)cot(x)) dx

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∫01(−cot⁡(x)csc⁡(x)+x) dx\int\limits_{0}^{1} \left(- \cot{\left(x \right)} \csc{\left(x \right)} + x\right)\, dx
Simplify
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

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

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

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

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

        1. The integral of cosecant times cotangent is cosecant:

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

        So, the result is: −csc⁡(x)- \csc{\left(x \right)}

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

    The result is: x22+csc⁡(x)\frac{x^{2}}{2} + \csc{\left(x \right)}

  2. Add the constant of integration:

    x22+csc⁡(x)+constant\frac{x^{2}}{2} + \csc{\left(x \right)}+ \mathrm{constant}

The answer is:

x22+csc⁡(x)+constant\frac{x^{2}}{2} + \csc{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              2         
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1sin⁡x+x22{{1}\over{\sin x}}+{{x^2}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-100000000100000000
Plot the graph f(x)
The answer [src] 
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Simplify
Numerical answer [src] 
-1.3793236779486e+19
-1.3793236779486e+19
The graph
Integral of (x-csc(x)cot(x)) dx

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

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