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sin(5*x-3)
Solving integrals/ sin(5*x-3)

Integral of sin(5*x-3) dx

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The solution

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∫01sin⁡(5x−3) dx\int\limits_{0}^{1} \sin{\left(5 x - 3 \right)}\, dx 
Integral(sin(5*x - 3), (x, 0, 1))
Detail solution

  1. Let u=5x−3u = 5 x - 3.

    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−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      
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∫sin⁡(5x−3) dx=C−cos⁡(5x−3)5\int \sin{\left(5 x - 3 \right)}\, dx = C - \frac{\cos{\left(5 x - 3 \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(2)   cos(3)
- ------ + ------
    5        5
cos⁡(3)5−cos⁡(2)5\frac{\cos{\left(3 \right)}}{5} - \frac{\cos{\left(2 \right)}}{5} 
=
= 
  cos(2)   cos(3)
- ------ + ------
    5        5
cos⁡(3)5−cos⁡(2)5\frac{\cos{\left(3 \right)}}{5} - \frac{\cos{\left(2 \right)}}{5} 
-cos(2)/5 + cos(3)/5
Numerical answer [src] 
-0.114769132010661
-0.114769132010661
The graph
Integral of sin(5*x-3) dx

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

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