Mister Exam

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Identical expressions
(three + two (sinx-cosx))
(3 plus 2( sinus of x minus co sinus of e of x))
(three plus two ( sinus of x minus co sinus of e of x))
3+2sinx-cosx
(3+2(sinx-cosx))dx
Similar expressions
(3-2(sinx-cosx))
(3+2(sinx+cosx))
1/(3+2sinx-cosx)

Integral of (3+2(sinx-cosx)) dx

The solution

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

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

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

$3 x - 2 \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)}$
Add the constant of integration:

$3 x - 2 \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}$

The answer is:

$3 x - 2 \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5 - 2*cos(1) - 2*sin(1)

$$- 2 \sin{\left(1 \right)} - 2 \cos{\left(1 \right)} + 5$$

5 - 2*cos(1) - 2*sin(1)

$$- 2 \sin{\left(1 \right)} - 2 \cos{\left(1 \right)} + 5$$

5 - 2*cos(1) - 2*sin(1)

Numerical answer [src]

2.23645341864793

2.23645341864793

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

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Integral of (3+2(sinx-cosx)) dx

Limits of integration:

The graph:

Piecewise:

The solution