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Identical expressions
three +5sinx+3cosx
3 plus 5 sinus of x plus 3 co sinus of e of x
three plus 5 sinus of x plus 3 co sinus of e of x
3+5sinx+3cosxdx
Similar expressions
3-5sinx+3cosx
dx/(3+5*sin(x)+3*cos(x))
3+5sinx-3cosx

Integral of 3+5sinx+3cosx dx

The solution

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  1                             
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 |  (3 + 5*sin(x) + 3*cos(x)) dx
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$$\int\limits_{0}^{1} \left(\left(5 \sin{\left(x \right)} + 3\right) + 3 \cos{\left(x \right)}\right)\, dx$$

Integral(3 + 5*sin(x) + 3*cos(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 \sin{\left(x \right)}\, dx = 5 \int \sin{\left(x \right)}\, dx$
    1. The integral of sine is negative cosine:
      
      $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
    So, the result is: $- 5 \cos{\left(x \right)}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 3\, dx = 3 x$
  The result is: $3 x - 5 \cos{\left(x \right)}$
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: $3 x + 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$
Add the constant of integration:

$3 x + 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$3 x + 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                            
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 | (3 + 5*sin(x) + 3*cos(x)) dx = C - 5*cos(x) + 3*x + 3*sin(x)
 |                                                             
/

$$\int \left(\left(5 \sin{\left(x \right)} + 3\right) + 3 \cos{\left(x \right)}\right)\, dx = C + 3 x + 3 \sin{\left(x \right)} - 5 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8 - 5*cos(1) + 3*sin(1)

$$- 5 \cos{\left(1 \right)} + 3 \sin{\left(1 \right)} + 8$$

8 - 5*cos(1) + 3*sin(1)

$$- 5 \cos{\left(1 \right)} + 3 \sin{\left(1 \right)} + 8$$

8 - 5*cos(1) + 3*sin(1)

Numerical answer [src]

7.82290142508299

7.82290142508299

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

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Identical expressions

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Integral of 3+5sinx+3cosx dx

Limits of integration:

The graph:

Piecewise:

The solution