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x+sqrt(x)
Solving integrals/ x+sqrt(x)

Integral of x+sqrt(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01(x+x) dx\int\limits_{0}^{1} \left(\sqrt{x} + x\right)\, dx 
Integral(x + sqrt(x), (x, 0, 1))
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:

      ∫x dx=2x323\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}

    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}

    The result is: 2x323+x22\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}

  2. Add the constant of integration:

    2x323+x22+constant\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}

The answer is:

2x323+x22+constant\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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x22+2 x323{{x^2}\over{2}}+{{2\,x^{{{3}\over{2}}}}\over{3}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
7/6
76{{7}\over{6}} 
=
= 
7/6
76\frac{7}{6}
Simplify
Numerical answer [src] 
1.16666666666667
1.16666666666667
The graph
Integral of x+sqrt(x) dx

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

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