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x^2+3x-5
Solving integrals/ x^2+3x-5

Integral of x^2+3x-5 dx

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The solution

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∫01((x2+3x)−5) dx\int\limits_{0}^{1} \left(\left(x^{2} + 3 x\right) - 5\right)\, dx 
Integral(x^2 + 3*x - 5, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      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}

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

        ∫3x dx=3∫x dx\int 3 x\, dx = 3 \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: 3x22\frac{3 x^{2}}{2}

      The result is: x33+3x22\frac{x^{3}}{3} + \frac{3 x^{2}}{2}

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

      ∫(−5) dx=−5x\int \left(-5\right)\, dx = - 5 x

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

  2. Now simplify:

    x(2x2+9x−30)6\frac{x \left(2 x^{2} + 9 x - 30\right)}{6}

  3. Add the constant of integration:

    x(2x2+9x−30)6+constant\frac{x \left(2 x^{2} + 9 x - 30\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2+9x−30)6+constant\frac{x \left(2 x^{2} + 9 x - 30\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | / 2          \                x    3*x 
 | \x  + 3*x - 5/ dx = C - 5*x + -- + ----
 |                               3     2  
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∫((x2+3x)−5) dx=C+x33+3x22−5x\int \left(\left(x^{2} + 3 x\right) - 5\right)\, dx = C + \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - 5 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-10
Plot the graph f(x)
The answer [src] 
-19/6
−196- \frac{19}{6} 
=
= 
-19/6
−196- \frac{19}{6} 
-19/6
Numerical answer [src] 
-3.16666666666667
-3.16666666666667
The graph
Integral of x^2+3x-5 dx

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

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