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sqrt(4x+5)
Solving integrals/ sqrt(4x+5)

Integral of sqrt(4x+5) dx

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
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 |    _________   
 |  \/ 4*x + 5  dx
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0
∫014x+5 dx\int\limits_{0}^{1} \sqrt{4 x + 5}\, dx 
Integral(sqrt(4*x + 5), (x, 0, 1))
Detail solution

  1. Let u=4x+5u = 4 x + 5.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    ∫u4 du\int \frac{\sqrt{u}}{4}\, du

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

      ∫u du=∫u du4\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{4}

      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: u326\frac{u^{\frac{3}{2}}}{6}

    Now substitute uu back in:

    (4x+5)326\frac{\left(4 x + 5\right)^{\frac{3}{2}}}{6}

  2. Now simplify:

    (4x+5)326\frac{\left(4 x + 5\right)^{\frac{3}{2}}}{6}

  3. Add the constant of integration:

    (4x+5)326+constant\frac{\left(4 x + 5\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer is:

(4x+5)326+constant\frac{\left(4 x + 5\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                               3/2
 |   _________          (4*x + 5)   
 | \/ 4*x + 5  dx = C + ------------
 |                           6      
/
∫4x+5 dx=C+(4x+5)326\int \sqrt{4 x + 5}\, dx = C + \frac{\left(4 x + 5\right)^{\frac{3}{2}}}{6}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.05.0
Plot the graph f(x)
The answer [src] 
        ___
9   5*\/ 5 
- - -------
2      6
92−556\frac{9}{2} - \frac{5 \sqrt{5}}{6} 
=
= 
        ___
9   5*\/ 5 
- - -------
2      6
92−556\frac{9}{2} - \frac{5 \sqrt{5}}{6} 
9/2 - 5*sqrt(5)/6
Numerical answer [src] 
2.63661001875018
2.63661001875018
The graph
Integral of sqrt(4x+5) dx

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

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