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(2x^2+3)dx
Solving integrals/ (2x^2+3)dx

Integral of (2x^2+3)dx dx

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The solution

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

  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 is the constant times the variable of integration:

      ∫3 dx=3x\int 3\, dx = 3 x

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

  2. Now simplify:

    x(2x2+9)3\frac{x \left(2 x^{2} + 9\right)}{3}

  3. Add the constant of integration:

    x(2x2+9)3+constant\frac{x \left(2 x^{2} + 9\right)}{3}+ \mathrm{constant}

The answer is:

x(2x2+9)3+constant\frac{x \left(2 x^{2} + 9\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
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 | \2*x  + 3/ dx = C + 3*x + ----
 |                            3  
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∫(2x2+3) dx=C+2x33+3x\int \left(2 x^{2} + 3\right)\, dx = C + \frac{2 x^{3}}{3} + 3 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
11/3
113\frac{11}{3} 
=
= 
11/3
113\frac{11}{3} 
11/3
Numerical answer [src] 
3.66666666666667
3.66666666666667
The graph
Integral of (2x^2+3)dx dx

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

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