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Solving integrals/ x²+4x

Integral of x²+4x dx

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The solution

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∫22(x2+4x) dx\int\limits_{2}^{2} \left(x^{2} + 4 x\right)\, dx 
Integral(x^2 + 4*x, (x, 2, 2))
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:

      ∫4x dx=4∫x dx\int 4 x\, dx = 4 \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: 2x22 x^{2}

    The result is: x33+2x2\frac{x^{3}}{3} + 2 x^{2}

  2. Now simplify:

    x2(x+6)3\frac{x^{2} \left(x + 6\right)}{3}

  3. Add the constant of integration:

    x2(x+6)3+constant\frac{x^{2} \left(x + 6\right)}{3}+ \mathrm{constant}

The answer is:

x2(x+6)3+constant\frac{x^{2} \left(x + 6\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2+4x) dx=C+x33+2x2\int \left(x^{2} + 4 x\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2}
Simplify
The graph
2.00002.01002.00102.00202.00302.00402.00502.00602.00702.00802.00901013
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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