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cos(4x+3)dx
Solving integrals/ cos(4x+3)dx

Integral of cos(4x+3)dx dx

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The solution

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 |  cos(4*x + 3)*1 dx
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∫01cos⁡(4x+3)1 dx\int\limits_{0}^{1} \cos{\left(4 x + 3 \right)} 1\, dx 
Integral(cos(4*x + 3)*1, (x, 0, 1))
Detail solution

  1. Let u=4x+3u = 4 x + 3.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    ∫cos⁡(u)16 du\int \frac{\cos{\left(u \right)}}{16}\, du

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

      ∫cos⁡(u)4 du=∫cos⁡(u) du4\int \frac{\cos{\left(u \right)}}{4}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}

      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)4\frac{\sin{\left(u \right)}}{4}

    Now substitute uu back in:

    sin⁡(4x+3)4\frac{\sin{\left(4 x + 3 \right)}}{4}

  2. Now simplify:

    sin⁡(4x+3)4\frac{\sin{\left(4 x + 3 \right)}}{4}

  3. Add the constant of integration:

    sin⁡(4x+3)4+constant\frac{\sin{\left(4 x + 3 \right)}}{4}+ \mathrm{constant}

The answer is:

sin⁡(4x+3)4+constant\frac{\sin{\left(4 x + 3 \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                    
 |                         sin(4*x + 3)
 | cos(4*x + 3)*1 dx = C + ------------
 |                              4      
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∫cos⁡(4x+3)1 dx=C+sin⁡(4x+3)4\int \cos{\left(4 x + 3 \right)} 1\, dx = C + \frac{\sin{\left(4 x + 3 \right)}}{4}
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(3)   sin(7)
- ------ + ------
    4        4
−sin⁡(3)4+sin⁡(7)4- \frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(7 \right)}}{4} 
=
= 
  sin(3)   sin(7)
- ------ + ------
    4        4
−sin⁡(3)4+sin⁡(7)4- \frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(7 \right)}}{4}
Упростить
Numerical answer [src] 
0.12896664766473
0.12896664766473
The graph
Integral of cos(4x+3)dx dx

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

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