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

Integral of 3x^2+2x dx

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The solution

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

      ∫3x2 dx=3∫x2 dx\int 3 x^{2}\, dx = 3 \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: x3x^{3}

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

      ∫2x dx=2∫x dx\int 2 x\, dx = 2 \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: x2x^{2}

    The result is: x3+x2x^{3} + x^{2}

  2. Now simplify:

    x2(x+1)x^{2} \left(x + 1\right)

  3. Add the constant of integration:

    x2(x+1)+constantx^{2} \left(x + 1\right)+ \mathrm{constant}

The answer is:

x2(x+1)+constantx^{2} \left(x + 1\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(3x2+2x) dx=C+x3+x2\int \left(3 x^{2} + 2 x\right)\, dx = C + x^{3} + x^{2}
Simplify
The graph
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The answer [src] 
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Numerical answer [src] 
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The graph
Integral of 3x^2+2x dx

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

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