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Solving integrals/ sqrt(4x+13)

Integral of sqrt(4x+13) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
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 |    __________   
 |  \/ 4*x + 13  dx
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/                  
0
∫014x+13 dx\int\limits_{0}^{1} \sqrt{4 x + 13}\, dx 
Integral(sqrt(4*x + 13), (x, 0, 1))
Detail solution

  1. Let u=4x+13u = 4 x + 13.

    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+13)326\frac{\left(4 x + 13\right)^{\frac{3}{2}}}{6}

  2. Now simplify:

    (4x+13)326\frac{\left(4 x + 13\right)^{\frac{3}{2}}}{6}

  3. Add the constant of integration:

    (4x+13)326+constant\frac{\left(4 x + 13\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer is:

(4x+13)326+constant\frac{\left(4 x + 13\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                   
 |                                 3/2
 |   __________          (4*x + 13)   
 | \/ 4*x + 13  dx = C + -------------
 |                             6      
/
∫4x+13 dx=C+(4x+13)326\int \sqrt{4 x + 13}\, dx = C + \frac{\left(4 x + 13\right)^{\frac{3}{2}}}{6}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020
Plot the graph f(x)
The answer [src] 
       ____        ____
  13*\/ 13    17*\/ 17 
- --------- + ---------
      6           6
−13136+17176- \frac{13 \sqrt{13}}{6} + \frac{17 \sqrt{17}}{6} 
=
= 
       ____        ____
  13*\/ 13    17*\/ 17 
- --------- + ---------
      6           6
−13136+17176- \frac{13 \sqrt{13}}{6} + \frac{17 \sqrt{17}}{6} 
-13*sqrt(13)/6 + 17*sqrt(17)/6
Numerical answer [src] 
3.87010484241139
3.87010484241139

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

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