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Integral of d{x}:
Integral of xe^(-4x)
Integral of x³lnxdx
Integral of sin(x/5)dx
Integral of cosx^2dx
Identical expressions
sin(x/ five)dx
sinus of (x divide by 5)dx
sinus of (x divide by five)dx
sinx/5dx
sin(x divide by 5)dx

Solving integrals/ sin(x/5)dx

Integral of sin(x/5)dx dx

The solution

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  1            
  /            
 |             
 |     /x\     
 |  sin|-|*1 dx
 |     \5/     
 |             
/              
0

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

Simplify

Detail solution

Let $u = \frac{x}{5}$ .

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

$\int 25 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 \sin{\left(u \right)}\, du = 5 \int \sin{\left(u \right)}\, du$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- 5 \cos{\left(u \right)}$
Now substitute $u$ back in:

$- 5 \cos{\left(\frac{x}{5} \right)}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          
 |                           
 |    /x\                 /x\
 | sin|-|*1 dx = C - 5*cos|-|
 |    \5/                 \5/
 |                           
/

$$-5\,\cos \left({{x}\over{5}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5 - 5*cos(1/5)

$$5-5\,\cos \left({{1}\over{5}}\right)$$

5 - 5*cos(1/5)

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

Simplify

Numerical answer [src]

0.0996671107937918

0.0996671107937918

The graph

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

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Identical expressions

Integral of sin(x/5)dx dx

Limits of integration:

The graph:

Piecewise:

The solution