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Solving integrals/ (2*x-3*y)-(x-y)

Integral of (2*x-3*y)-(x-y) dx

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The solution

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 |  (2*x - 3*y + -x + y) dx
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∫01((−x+y)+(2x−3y)) dx\int\limits_{0}^{1} \left(\left(- x + y\right) + \left(2 x - 3 y\right)\right)\, dx 
Integral(2*x - 3*y - x + y, (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:

        ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \int x\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

        So, the result is: −x22- \frac{x^{2}}{2}

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

        ∫y dx=xy\int y\, dx = x y

      The result is: −x22+xy- \frac{x^{2}}{2} + x y

    1. Integrate term-by-term:

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

        ∫2x dx=2∫x dx\int 2 x\, dx = 2 \int x\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

        So, the result is: x2x^{2}

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

        ∫(−3y) dx=−3xy\int \left(- 3 y\right)\, dx = - 3 x y

      The result is: x2−3xyx^{2} - 3 x y

    The result is: x22−2xy\frac{x^{2}}{2} - 2 x y

  2. Now simplify:

    x(x−4y)2\frac{x \left(x - 4 y\right)}{2}

  3. Add the constant of integration:

    x(x−4y)2+constant\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}

The answer is:

x(x−4y)2+constant\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               2        
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 | (2*x - 3*y + -x + y) dx = C + -- - 2*x*y
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∫((−x+y)+(2x−3y)) dx=C+x22−2xy\int \left(\left(- x + y\right) + \left(2 x - 3 y\right)\right)\, dx = C + \frac{x^{2}}{2} - 2 x y
Simplify
The answer [src] 
1/2 - 2*y
12−2y\frac{1}{2} - 2 y 
=
= 
1/2 - 2*y
12−2y\frac{1}{2} - 2 y 
1/2 - 2*y

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

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