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Cos(5x-6)
Solving integrals/ Cos(5x-6)

Integral of Cos(5x-6) dx

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The solution

You have entered [src] 
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 |  cos(5*x - 6) dx
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∫01cos⁡(5x−6) dx\int\limits_{0}^{1} \cos{\left(5 x - 6 \right)}\, dx 
Integral(cos(5*x - 1*6), (x, 0, 1))
Detail solution

  1. Let u=5x−6u = 5 x - 6.

    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−6)5\frac{\sin{\left(5 x - 6 \right)}}{5}

  2. Now simplify:

    sin⁡(5x−6)5\frac{\sin{\left(5 x - 6 \right)}}{5}

  3. Add the constant of integration:

    sin⁡(5x−6)5+constant\frac{\sin{\left(5 x - 6 \right)}}{5}+ \mathrm{constant}

The answer is:

sin⁡(5x−6)5+constant\frac{\sin{\left(5 x - 6 \right)}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                       sin(5*x - 6)
 | cos(5*x - 6) dx = C + ------------
 |                            5      
/
sin⁡(5 x−6)5{{\sin \left(5\,x-6\right)}\over{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(1)   sin(6)
- ------ + ------
    5        5
sin⁡6−sin⁡15{{\sin 6-\sin 1}\over{5}} 
=
= 
  sin(1)   sin(6)
- ------ + ------
    5        5
−sin⁡(1)5+sin⁡(6)5- \frac{\sin{\left(1 \right)}}{5} + \frac{\sin{\left(6 \right)}}{5}
Simplify
Numerical answer [src] 
-0.224177296601364
-0.224177296601364
The graph
Integral of Cos(5x-6) dx

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

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