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(cosx)/ four +3sinx
( co sinus of e of x) divide by 4 plus 3 sinus of x
( co sinus of e of x) divide by four plus 3 sinus of x
cosx/4+3sinx
(cosx) divide by 4+3sinx
(cosx)/4+3sinxdx
Similar expressions
(cosx)/4-3sinx

Solving integrals/ (cosx)/4+3sinx

Integral of (cosx)/4+3sinx dx

The solution

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  1                       
  /                       
 |                        
 |  /cos(x)           \   
 |  |------ + 3*sin(x)| dx
 |  \  4              /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(3 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{4}\right)\, dx$$

Integral(cos(x)/4 + 3*sin(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:
  
  $\int 3 \sin{\left(x \right)}\, dx = 3 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 3 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(x \right)}}{4}\, dx = \frac{\int \cos{\left(x \right)}\, dx}{4}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $\frac{\sin{\left(x \right)}}{4}$
The result is: $\frac{\sin{\left(x \right)}}{4} - 3 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{\sin{\left(x \right)}}{4} - 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(x \right)}}{4} - 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /cos(x)           \                     sin(x)
 | |------ + 3*sin(x)| dx = C - 3*cos(x) + ------
 | \  4              /                       4   
 |                                               
/

$${{\sin x}\over{4}}-3\,\cos x$$

Simplify

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Plot the graph f(x)

The answer [src]

               sin(1)
3 - 3*cos(1) + ------
                 4

$${{\sin 1-12\,\cos 1+12}\over{4}}$$

               sin(1)
3 - 3*cos(1) + ------
                 4

$$- 3 \cos{\left(1 \right)} + \frac{\sin{\left(1 \right)}}{4} + 3$$

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Numerical answer [src]

1.58946082859755

1.58946082859755

The graph

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

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Integral of (cosx)/4+3sinx dx

Limits of integration:

The graph:

Piecewise:

The solution