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Integral of (3sinx-e^x+2)dx dx

The solution

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

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

Integral(3*sin(x) - E^x + 2, (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:
    
    $\int \left(- e^{x}\right)\, dx = - \int e^{x}\, dx$
    1. The integral of the exponential function is itself.
      
      $\int e^{x}\, dx = e^{x}$
    So, the result is: $- e^{x}$
  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: $- 3 \cos{\left(x \right)}$
  The result is: $- e^{x} - 3 \cos{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
The result is: $2 x - e^{x} - 3 \cos{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(\left(- e^{x} + 3 \sin{\left(x \right)}\right) + 2\right)\, dx = C + 2 x - e^{x} - 3 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

6 - E - 3*cos(1)

$$- e - 3 \cos{\left(1 \right)} + 6$$

6 - E - 3*cos(1)

$$- e - 3 \cos{\left(1 \right)} + 6$$

6 - E - 3*cos(1)

Numerical answer [src]

1.66081125393654

1.66081125393654

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

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Integral of (3sinx-e^x+2)dx dx

Limits of integration:

The graph:

Piecewise:

The solution