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Solving integrals/ (3sinx-e^x+2)dx

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  \3*sin(x) - E  + 2/ dx
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∫01((−ex+3sin⁡(x))+2) dx\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

  1. 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:

        ∫(−ex) dx=−∫ex dx\int \left(- e^{x}\right)\, dx = - \int e^{x}\, dx

        1. The integral of the exponential function is itself.

          ∫ex dx=ex\int e^{x}\, dx = e^{x}

        So, the result is: −ex- e^{x}

      1. The integral of a constant times a function is the constant times the integral of the function:

        ∫3sin⁡(x) dx=3∫sin⁡(x) dx\int 3 \sin{\left(x \right)}\, dx = 3 \int \sin{\left(x \right)}\, dx

        1. The integral of sine is negative cosine:

          ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

        So, the result is: −3cos⁡(x)- 3 \cos{\left(x \right)}

      The result is: −ex−3cos⁡(x)- e^{x} - 3 \cos{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      ∫2 dx=2x\int 2\, dx = 2 x

    The result is: 2x−ex−3cos⁡(x)2 x - e^{x} - 3 \cos{\left(x \right)}

  2. Add the constant of integration:

    2x−ex−3cos⁡(x)+constant2 x - e^{x} - 3 \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

2x−ex−3cos⁡(x)+constant2 x - e^{x} - 3 \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                
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 | /            x    \           x                 
 | \3*sin(x) - E  + 2/ dx = C - e  - 3*cos(x) + 2*x
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∫((−ex+3sin⁡(x))+2) dx=C+2x−ex−3cos⁡(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
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
6 - E - 3*cos(1)
−e−3cos⁡(1)+6- e - 3 \cos{\left(1 \right)} + 6 
=
= 
6 - E - 3*cos(1)
−e−3cos⁡(1)+6- 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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