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cos(7x+2)
Solving integrals/ cos(7x+2)

Integral of cos(7x+2) dx

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The solution

You have entered [src] 
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∫01cos⁡(7x+2) dx\int\limits_{0}^{1} \cos{\left(7 x + 2 \right)}\, dx 
Integral(cos(7*x + 2), (x, 0, 1))
Detail solution

  1. Let u=7x+2u = 7 x + 2.

    Then let du=7dxdu = 7 dx and substitute du7\frac{du}{7}:

    ∫cos⁡(u)49 du\int \frac{\cos{\left(u \right)}}{49}\, du

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

      ∫cos⁡(u)7 du=∫cos⁡(u) du7\int \frac{\cos{\left(u \right)}}{7}\, du = \frac{\int \cos{\left(u \right)}\, du}{7}

      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)7\frac{\sin{\left(u \right)}}{7}

    Now substitute uu back in:

    sin⁡(7x+2)7\frac{\sin{\left(7 x + 2 \right)}}{7}

  2. Now simplify:

    sin⁡(7x+2)7\frac{\sin{\left(7 x + 2 \right)}}{7}

  3. Add the constant of integration:

    sin⁡(7x+2)7+constant\frac{\sin{\left(7 x + 2 \right)}}{7}+ \mathrm{constant}

The answer is:

sin⁡(7x+2)7+constant\frac{\sin{\left(7 x + 2 \right)}}{7}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                       sin(7*x + 2)
 | cos(7*x + 2) dx = C + ------------
 |                            7      
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sin⁡(7 x+2)7{{\sin \left(7\,x+2\right)}\over{7}}
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(2)   sin(9)
- ------ + ------
    7        7
sin⁡97−sin⁡27{{\sin 9}\over{7}}-{{\sin 2}\over{7}} 
=
= 
  sin(2)   sin(9)
- ------ + ------
    7        7
−sin⁡(2)7+sin⁡(9)7- \frac{\sin{\left(2 \right)}}{7} + \frac{\sin{\left(9 \right)}}{7}
Simplify
Numerical answer [src] 
-0.0710255630834179
-0.0710255630834179
The graph
Integral of cos(7x+2) dx

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

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