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Identical expressions
sinx/ four +5cosx
sinus of x divide by 4 plus 5 co sinus of e of x
sinus of x divide by four plus 5 co sinus of e of x
sinx divide by 4+5cosx
sinx/4+5cosxdx
Similar expressions
sinx/4-5cosx

Solving integrals/ sinx/4+5cosx

Integral of sinx/4+5cosx dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /sin(x)           \   
 |  |------ + 5*cos(x)| dx
 |  \  4              /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(\frac{\sin{\left(x \right)}}{4} + 5 \cos{\left(x \right)}\right)\, dx$$

Integral(sin(x)/4 + 5*cos(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(x \right)}}{4}\, dx = \frac{\int \sin{\left(x \right)}\, dx}{4}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- \frac{\cos{\left(x \right)}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 \cos{\left(x \right)}\, dx = 5 \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $5 \sin{\left(x \right)}$
The result is: $5 \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{4}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /sin(x)           \                     cos(x)
 | |------ + 5*cos(x)| dx = C + 5*sin(x) - ------
 | \  4              /                       4   
 |                                               
/

$$5\,\sin x-{{\cos x}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1              cos(1)
- + 5*sin(1) - ------
4                4

$${{20\,\sin 1-\cos 1+1}\over{4}}$$

1              cos(1)
- + 5*sin(1) - ------
4                4

$$- \frac{\cos{\left(1 \right)}}{4} + \frac{1}{4} + 5 \sin{\left(1 \right)}$$

Simplify

Numerical answer [src]

4.32227934757245

4.32227934757245

The graph

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

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Integral of sinx/4+5cosx dx

Limits of integration:

The graph:

Piecewise:

The solution