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cos(5*x)
Solving integrals/ cos(5*x)

Integral of cos(5*x) dx

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The solution

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∫01cos⁡(5x) dx\int\limits_{0}^{1} \cos{\left(5 x \right)}\, dx 
Integral(cos(5*x), (x, 0, 1))
Detail solution

  1. Let u=5xu = 5 x.

    Then let du=5dxdu = 5 dx and substitute du5\frac{du}{5}:

    ∫cos⁡(u)25 du\int \frac{\cos{\left(u \right)}}{25}\, du

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

      ∫cos⁡(u)5 du=∫cos⁡(u) du5\int \frac{\cos{\left(u \right)}}{5}\, du = \frac{\int \cos{\left(u \right)}\, du}{5}

      1. The integral of cosine is sine:

        ∫cos⁡(u) du=sin⁡(u)\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}

      So, the result is: sin⁡(u)5\frac{\sin{\left(u \right)}}{5}

    Now substitute uu back in:

    sin⁡(5x)5\frac{\sin{\left(5 x \right)}}{5}

  2. Add the constant of integration:

    sin⁡(5x)5+constant\frac{\sin{\left(5 x \right)}}{5}+ \mathrm{constant}

The answer is:

sin⁡(5x)5+constant\frac{\sin{\left(5 x \right)}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 |                   sin(5*x)
 | cos(5*x) dx = C + --------
 |                      5    
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∫cos⁡(5x) dx=C+sin⁡(5x)5\int \cos{\left(5 x \right)}\, dx = C + \frac{\sin{\left(5 x \right)}}{5}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
sin(5)
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  5
sin⁡(5)5\frac{\sin{\left(5 \right)}}{5} 
=
= 
sin(5)
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  5
sin⁡(5)5\frac{\sin{\left(5 \right)}}{5}
Упростить
Numerical answer [src] 
-0.191784854932628
-0.191784854932628
The graph
Integral of cos(5*x) dx

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

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