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

Integral of x^2+3x dx

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The solution

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∫01(x2+3x) dx\int\limits_{0}^{1} \left(x^{2} + 3 x\right)\, dx 
Integral(x^2 + 3*x, (x, 0, 1))
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:

      ∫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}

  2. Now simplify:

    x2⋅(2x+9)6\frac{x^{2} \cdot \left(2 x + 9\right)}{6}

  3. Add the constant of integration:

    x2⋅(2x+9)6+constant\frac{x^{2} \cdot \left(2 x + 9\right)}{6}+ \mathrm{constant}

The answer is:

x2⋅(2x+9)6+constant\frac{x^{2} \cdot \left(2 x + 9\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                      3      2
 | / 2      \          x    3*x 
 | \x  + 3*x/ dx = C + -- + ----
 |                     3     2  
/
x33+3 x22{{x^3}\over{3}}+{{3\,x^2}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
11/6
116{{11}\over{6}} 
=
= 
11/6
116\frac{11}{6}
Упростить
Numerical answer [src] 
1.83333333333333
1.83333333333333
The graph
Integral of x^2+3x dx

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

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