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(2x^2-5x-7)dx
Solving integrals/ (2x^2-5x-7)dx

Integral of (2x^2-5x-7)dx dx

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∫−11((2x2−5x)−7) dx\int\limits_{-1}^{1} \left(\left(2 x^{2} - 5 x\right) - 7\right)\, dx 
Integral(2*x^2 - 5*x - 7, (x, -1, 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:

        ∫2x2 dx=2∫x2 dx\int 2 x^{2}\, dx = 2 \int x^{2}\, dx

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

          ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

        So, the result is: 2x33\frac{2 x^{3}}{3}

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

        ∫(−5x) dx=−5∫x dx\int \left(- 5 x\right)\, dx = - 5 \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: −5x22- \frac{5 x^{2}}{2}

      The result is: 2x33−5x22\frac{2 x^{3}}{3} - \frac{5 x^{2}}{2}

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

      ∫(−7) dx=−7x\int \left(-7\right)\, dx = - 7 x

    The result is: 2x33−5x22−7x\frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x

  2. Now simplify:

    x(4x2−15x−42)6\frac{x \left(4 x^{2} - 15 x - 42\right)}{6}

  3. Add the constant of integration:

    x(4x2−15x−42)6+constant\frac{x \left(4 x^{2} - 15 x - 42\right)}{6}+ \mathrm{constant}

The answer is:

x(4x2−15x−42)6+constant\frac{x \left(4 x^{2} - 15 x - 42\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | /   2          \                5*x    2*x 
 | \2*x  - 5*x - 7/ dx = C - 7*x - ---- + ----
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∫((2x2−5x)−7) dx=C+2x33−5x22−7x\int \left(\left(2 x^{2} - 5 x\right) - 7\right)\, dx = C + \frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.8-2020
Plot the graph f(x)
The answer [src] 
-38/3
−383- \frac{38}{3} 
=
= 
-38/3
−383- \frac{38}{3} 
-38/3
Numerical answer [src] 
-12.6666666666667
-12.6666666666667
The graph
Integral of (2x^2-5x-7)dx dx

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

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