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Identical expressions
dx/2sinx+3cosx
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Similar expressions
dx/2sinx-3cosx

Solving integrals/ dx/2sinx+3cosx

Integral of dx/2sinx+3cosx dx

The solution

You have entered [src]

  1                           
  /                           
 |                            
 |  /  1                  \   
 |  |1*-*sin(x) + 3*cos(x)| dx
 |  \  2                  /   
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(1 \cdot \frac{1}{2} \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)\, dx$$

Simplify

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 1 \cdot \frac{1}{2} \sin{\left(x \right)}\, dx = \frac{\int \sin{\left(x \right)}\, dx}{2}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- \frac{\cos{\left(x \right)}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 \cos{\left(x \right)}\, dx = 3 \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $3 \sin{\left(x \right)}$
The result is: $3 \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2}$
Add the constant of integration:

$3 \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$3 \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                  
 |                                                   
 | /  1                  \                     cos(x)
 | |1*-*sin(x) + 3*cos(x)| dx = C + 3*sin(x) - ------
 | \  2                  /                       2   
 |                                                   
/

$$3\,\sin x-{{\cos x}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1              cos(1)
- + 3*sin(1) - ------
2                2

$${{6\,\sin 1-\cos 1+1}\over{2}}$$

1              cos(1)
- + 3*sin(1) - ------
2                2

$$- \frac{\cos{\left(1 \right)}}{2} + \frac{1}{2} + 3 \sin{\left(1 \right)}$$

Simplify

Numerical answer [src]

2.75426180148962

2.75426180148962

The graph

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

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Identical expressions

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Integral of dx/2sinx+3cosx dx

Limits of integration:

The graph:

Piecewise:

The solution