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x^2+7x
Solving integrals/ x^2+7x

Integral of x^2+7x dx

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The solution

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-1
∫−13(x2+7x) dx\int\limits_{-1}^{3} \left(x^{2} + 7 x\right)\, dx 
Integral(x^2 + 7*x, (x, -1, 3))
Detail solution

  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:

      ∫7x dx=7∫x dx\int 7 x\, dx = 7 \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: 7x22\frac{7 x^{2}}{2}

    The result is: x33+7x22\frac{x^{3}}{3} + \frac{7 x^{2}}{2}

  2. Now simplify:

    x2⋅(2x+21)6\frac{x^{2} \cdot \left(2 x + 21\right)}{6}

  3. Add the constant of integration:

    x2⋅(2x+21)6+constant\frac{x^{2} \cdot \left(2 x + 21\right)}{6}+ \mathrm{constant}

The answer is:

x2⋅(2x+21)6+constant\frac{x^{2} \cdot \left(2 x + 21\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                      3      2
 | / 2      \          x    7*x 
 | \x  + 7*x/ dx = C + -- + ----
 |                     3     2  
/
∫(x2+7x) dx=C+x33+7x22\int \left(x^{2} + 7 x\right)\, dx = C + \frac{x^{3}}{3} + \frac{7 x^{2}}{2}
Simplify
The graph
-1.0-0.53.00.00.51.01.52.02.5-5050
Plot the graph f(x)
The answer [src] 
112/3
1123\frac{112}{3} 
=
= 
112/3
1123\frac{112}{3}
Упростить
Numerical answer [src] 
37.3333333333333
37.3333333333333
The graph
Integral of x^2+7x dx

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

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