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Solving integrals/ (5cscxcotx-4sec²x)dx

Integral of (5cscxcotx-4sec²x)dx dx

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The solution

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∫01(cot⁡(x)5csc⁡(x)−4sec⁡2(x)) dx\int\limits_{0}^{1} \left(\cot{\left(x \right)} 5 \csc{\left(x \right)} - 4 \sec^{2}{\left(x \right)}\right)\, dx 
Integral((5*csc(x))*cot(x) - 4*sec(x)^2, (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:

      ∫cot⁡(x)5csc⁡(x) dx=−5∫(−cot⁡(x)csc⁡(x)) dx\int \cot{\left(x \right)} 5 \csc{\left(x \right)}\, dx = - 5 \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: −5csc⁡(x)- 5 \csc{\left(x \right)}

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

      ∫(−4sec⁡2(x)) dx=−4∫sec⁡2(x) dx\int \left(- 4 \sec^{2}{\left(x \right)}\right)\, dx = - 4 \int \sec^{2}{\left(x \right)}\, dx

      1. ∫sec⁡2(x) dx=tan⁡(x)\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}

      So, the result is: −4tan⁡(x)- 4 \tan{\left(x \right)}

    The result is: −4tan⁡(x)−5csc⁡(x)- 4 \tan{\left(x \right)} - 5 \csc{\left(x \right)}

  2. Now simplify:

    −4tan⁡(x)−5sin⁡(x)- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}

  3. Add the constant of integration:

    −4tan⁡(x)−5sin⁡(x)+constant- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}+ \mathrm{constant}

The answer is:

−4tan⁡(x)−5sin⁡(x)+constant- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \5*csc(x)*cot(x) - 4*sec (x)/ dx = C - 5*csc(x) - 4*tan(x)
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∫(cot⁡(x)5csc⁡(x)−4sec⁡2(x)) dx=C−4tan⁡(x)−5csc⁡(x)\int \left(\cot{\left(x \right)} 5 \csc{\left(x \right)} - 4 \sec^{2}{\left(x \right)}\right)\, dx = C - 4 \tan{\left(x \right)} - 5 \csc{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-500000000500000000
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
6.89661838974298e+19
6.89661838974298e+19

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

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