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(10x^4+3x^2+4)

Integral of (10x^4+3x^2+4) dx

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The solution

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02(10x4+3x2+4)dx\int\limits_{0}^{2} \left(10 x^{4} + 3 x^{2} + 4\right)\, dx
Integral(10*x^4 + 3*x^2 + 4, (x, 0, 2))
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:

      10x4dx=10x4dx\int 10 x^{4}\, dx = 10 \int x^{4}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

        x4dx=x55\int x^{4}\, dx = \frac{x^{5}}{5}

      So, the result is: 2x52 x^{5}

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

      3x2dx=3x2dx\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 n1n \neq -1:

        x2dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: x3x^{3}

    1. The integral of a constant is the constant times the variable of integration:

      4dx=4x\int 4\, dx = 4 x

    The result is: 2x5+x3+4x2 x^{5} + x^{3} + 4 x

  2. Now simplify:

    x(2x4+x2+4)x \left(2 x^{4} + x^{2} + 4\right)

  3. Add the constant of integration:

    x(2x4+x2+4)+constantx \left(2 x^{4} + x^{2} + 4\right)+ \mathrm{constant}


The answer is:

x(2x4+x2+4)+constantx \left(2 x^{4} + x^{2} + 4\right)+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                           
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 | \10*x  + 3*x  + 4/ dx = C + x  + 2*x  + 4*x
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2x5+x3+4x2\,x^5+x^3+4\,x
The graph
0.02.00.20.40.60.81.01.21.41.61.80200
The answer [src]
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80
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Numerical answer [src]
80.0
80.0
The graph
Integral of (10x^4+3x^2+4) dx

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