Integral of sin(1-5x)dx dx

The solution

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 |  sin(1 - 5*x) dx
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$$\int\limits_{0}^{0} \sin{\left(1 - 5 x \right)}\, dx$$

Integral(sin(1 - 5*x), (x, 0, 0))

Detail solution

Let $u = 1 - 5 x$ .

Then let $du = - 5 dx$ and substitute $- \frac{du}{5}$ :

$\int \left(- \frac{\sin{\left(u \right)}}{5}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = - \frac{\int \sin{\left(u \right)}\, du}{5}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $\frac{\cos{\left(u \right)}}{5}$
Now substitute $u$ back in:

$\frac{\cos{\left(5 x - 1 \right)}}{5}$
Add the constant of integration:

$\frac{\cos{\left(5 x - 1 \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{\cos{\left(5 x - 1 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                       cos(-1 + 5*x)
 | sin(1 - 5*x) dx = C + -------------
 |                             5      
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$$\int \sin{\left(1 - 5 x \right)}\, dx = C + \frac{\cos{\left(5 x - 1 \right)}}{5}$$

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Numerical answer [src]

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

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Integral of sin(1-5x)dx dx

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