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sqrt(1+8x)
Solving integrals/ sqrt(1+8x)

Integral of sqrt(1+8x) dx

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The solution

You have entered [src] 
  1               
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 |    _________   
 |  \/ 1 + 8*x  dx
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∫018x+1 dx\int\limits_{0}^{1} \sqrt{8 x + 1}\, dx 
Integral(sqrt(1 + 8*x), (x, 0, 1))
Detail solution

  1. Let u=8x+1u = 8 x + 1.

    Then let du=8dxdu = 8 dx and substitute du8\frac{du}{8}:

    ∫u8 du\int \frac{\sqrt{u}}{8}\, du

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

      ∫u du=∫u du8\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{8}

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=2u323\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}

      So, the result is: u3212\frac{u^{\frac{3}{2}}}{12}

    Now substitute uu back in:

    (8x+1)3212\frac{\left(8 x + 1\right)^{\frac{3}{2}}}{12}

  2. Add the constant of integration:

    (8x+1)3212+constant\frac{\left(8 x + 1\right)^{\frac{3}{2}}}{12}+ \mathrm{constant}

The answer is:

(8x+1)3212+constant\frac{\left(8 x + 1\right)^{\frac{3}{2}}}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                               3/2
 |   _________          (1 + 8*x)   
 | \/ 1 + 8*x  dx = C + ------------
 |                           12     
/
∫8x+1 dx=C+(8x+1)3212\int \sqrt{8 x + 1}\, dx = C + \frac{\left(8 x + 1\right)^{\frac{3}{2}}}{12}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
13/6
136\frac{13}{6} 
=
= 
13/6
136\frac{13}{6} 
13/6
Numerical answer [src] 
2.16666666666667
2.16666666666667
The graph
Integral of sqrt(1+8x) dx

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

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