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

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

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The solution

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

  1. Rewrite the integrand:

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

  2. 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:

      ∫x4 dx=x55\int x^{4}\, dx = \frac{x^{5}}{5}

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

      ∫4x2 dx=4∫x2 dx\int 4 x^{2}\, dx = 4 \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: 4x33\frac{4 x^{3}}{3}

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

      ∫4 dx=4x\int 4\, dx = 4 x

    The result is: x55+4x33+4x\frac{x^{5}}{5} + \frac{4 x^{3}}{3} + 4 x

  3. Now simplify:

    x(3x4+20x2+60)15\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}

  4. Add the constant of integration:

    x(3x4+20x2+60)15+constant\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}+ \mathrm{constant}

The answer is:

x(3x4+20x2+60)15+constant\frac{x \left(3 x^{4} + 20 x^{2} + 60\right)}{15}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2+2)2 dx=C+x55+4x33+4x\int \left(x^{2} + 2\right)^{2}\, dx = C + \frac{x^{5}}{5} + \frac{4 x^{3}}{3} + 4 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
83
--
15
8315\frac{83}{15} 
=
= 
83
--
15
8315\frac{83}{15} 
83/15
Numerical answer [src] 
5.53333333333333
5.53333333333333
The graph
Integral of (x^2+2)^2 dx

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

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