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sqrtx+sqrtx+1
Solving integrals/ sqrtx+sqrtx+1

Integral of sqrtx+sqrtx+1 dx

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The graph:

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Piecewise:

The solution

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

  1. Integrate term-by-term:

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

      The result is: 4x323\frac{4 x^{\frac{3}{2}}}{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: 4x323+x\frac{4 x^{\frac{3}{2}}}{3} + x

  2. Add the constant of integration:

    4x323+x+constant\frac{4 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}

The answer is:

4x323+x+constant\frac{4 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫((x+x)+1) dx=C+4x323+x\int \left(\left(\sqrt{x} + \sqrt{x}\right) + 1\right)\, dx = C + \frac{4 x^{\frac{3}{2}}}{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] 
7/3
73\frac{7}{3} 
=
= 
7/3
73\frac{7}{3} 
7/3
Numerical answer [src] 
2.33333333333333
2.33333333333333
The graph
Integral of sqrtx+sqrtx+1 dx

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

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