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sin(5x+4)
Solving integrals/ sin(5x+4)

Integral of sin(5x+4) dx

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The solution

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∫01sin⁡(5x+4) dx\int\limits_{0}^{1} \sin{\left(5 x + 4 \right)}\, dx 
Integral(sin(5*x + 4), (x, 0, 1))
Detail solution

  1. Let u=5x+4u = 5 x + 4.

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

    ∫sin⁡(u)5 du\int \frac{\sin{\left(u \right)}}{5}\, du

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

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

      1. The integral of sine is negative cosine:

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

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

    Now substitute uu back in:

    −cos⁡(5x+4)5- \frac{\cos{\left(5 x + 4 \right)}}{5}

  2. Now simplify:

    −cos⁡(5x+4)5- \frac{\cos{\left(5 x + 4 \right)}}{5}

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                                  
 |                       cos(5*x + 4)
 | sin(5*x + 4) dx = C - ------------
 |                            5      
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∫sin⁡(5x+4) dx=C−cos⁡(5x+4)5\int \sin{\left(5 x + 4 \right)}\, dx = C - \frac{\cos{\left(5 x + 4 \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] 
  cos(9)   cos(4)
- ------ + ------
    5        5
cos⁡(4)5−cos⁡(9)5\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(9 \right)}}{5} 
=
= 
  cos(9)   cos(4)
- ------ + ------
    5        5
cos⁡(4)5−cos⁡(9)5\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(9 \right)}}{5} 
-cos(9)/5 + cos(4)/5
Numerical answer [src] 
0.051497328204213
0.051497328204213
The graph
Integral of sin(5x+4) dx

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

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