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sqrt(x)+sqrt(x^3)
Solving integrals/ sqrt(x)+sqrt(x^3)

Integral of sqrt(x)+sqrt(x^3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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∫01(x+x3) dx\int\limits_{0}^{1} \left(\sqrt{x} + \sqrt{x^{3}}\right)\, dx 
Integral(sqrt(x) + sqrt(x^3), (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. Don't know the steps in finding this integral.

      But the integral is

      2xx35\frac{2 x \sqrt{x^{3}}}{5}

    The result is: 2x323+2xx35\frac{2 x^{\frac{3}{2}}}{3} + \frac{2 x \sqrt{x^{3}}}{5}

  2. Add the constant of integration:

    2x323+2xx35+constant\frac{2 x^{\frac{3}{2}}}{3} + \frac{2 x \sqrt{x^{3}}}{5}+ \mathrm{constant}

The answer is:

2x323+2xx35+constant\frac{2 x^{\frac{3}{2}}}{3} + \frac{2 x \sqrt{x^{3}}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \\/ x  + \/  x  / dx = C + ------ + -----------
 |                              3           5     
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∫(x+x3) dx=C+2x323+2xx35\int \left(\sqrt{x} + \sqrt{x^{3}}\right)\, dx = C + \frac{2 x^{\frac{3}{2}}}{3} + \frac{2 x \sqrt{x^{3}}}{5}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
16
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15
1615\frac{16}{15} 
=
= 
16
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15
1615\frac{16}{15} 
16/15
Numerical answer [src] 
1.06666666666667
1.06666666666667
The graph
Integral of sqrt(x)+sqrt(x^3) dx

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

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