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sin(5x+3)
Solving integrals/ sin(5x+3)

Integral of sin(5x+3) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  sin(5*x + 3) dx
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∫01sin⁡(5x+3) dx\int\limits_{0}^{1} \sin{\left(5 x + 3 \right)}\, dx
Simplify
Detail solution

  1. Let u=5x+3u = 5 x + 3.

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

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

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

      ∫sin⁡(u)5 du=∫sin⁡(u) du5\int \frac{\sin{\left(u \right)}}{5}\, 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+3)5- \frac{\cos{\left(5 x + 3 \right)}}{5}

  2. Now simplify:

    −cos⁡(5x+3)5- \frac{\cos{\left(5 x + 3 \right)}}{5}

  3. Add the constant of integration:

    −cos⁡(5x+3)5+constant- \frac{\cos{\left(5 x + 3 \right)}}{5}+ \mathrm{constant}

The answer is:

−cos⁡(5x+3)5+constant- \frac{\cos{\left(5 x + 3 \right)}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                       cos(5*x + 3)
 | sin(5*x + 3) dx = C - ------------
 |                            5      
/
−cos⁡(5 x+3)5-{{\cos \left(5\,x+3\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] 
  cos(8)   cos(3)
- ------ + ------
    5        5
cos⁡3−cos⁡85{{\cos 3-\cos 8}\over{5}} 
=
= 
  cos(8)   cos(3)
- ------ + ------
    5        5
cos⁡(3)5−cos⁡(8)5\frac{\cos{\left(3 \right)}}{5} - \frac{\cos{\left(8 \right)}}{5}
Simplify
Numerical answer [src] 
-0.168898492558366
-0.168898492558366
The graph
Integral of sin(5x+3) dx

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

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