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(x^2+1)^2
Solving integrals/ (x^2+1)^2

Integral of (x^2+1)^2 dx

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The solution

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

  1. Rewrite the integrand:

    (x2+1)2=x4+2x2+1\left(x^{2} + 1\right)^{2} = x^{4} + 2 x^{2} + 1

  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:

      ∫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:

      ∫1 dx=x\int 1\, dx = x

    The result is: x55+2x33+x\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x

  3. Add the constant of integration:

    x55+2x33+x+constant\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}

The answer is:

x55+2x33+x+constant\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2+1)2 dx=C+x55+2x33+x\int \left(x^{2} + 1\right)^{2}\, dx = C + \frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
28
--
15
2815\frac{28}{15} 
=
= 
28
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15
2815\frac{28}{15} 
28/15
Numerical answer [src] 
1.86666666666667
1.86666666666667
The graph
Integral of (x^2+1)^2 dx

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

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