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Solving integrals/ 3dx/sqrt2x-5

Integral of 3dx/sqrt2x-5 dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  /   3       \   
 |  |------- - 5| dx
 |  |  _____    |   
 |  \\/ 2*x     /   
 |                  
/                   
0
∫01(−5+32x) dx\int\limits_{0}^{1} \left(-5 + \frac{3}{\sqrt{2 x}}\right)\, dx 
Integral(3/sqrt(2*x) - 5, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

      ∫(−5) dx=−5x\int \left(-5\right)\, dx = - 5 x

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

      ∫32x dx=3∫12x dx\int \frac{3}{\sqrt{2 x}}\, dx = 3 \int \frac{1}{\sqrt{2 x}}\, dx

      1. Let u=2xu = \sqrt{2 x}.

        Then let du=2dx2xdu = \frac{\sqrt{2} dx}{2 \sqrt{x}} and substitute dudu:

        ∫1 du\int 1\, du

        1. The integral of a constant is the constant times the variable of integration:

          ∫1 du=u\int 1\, du = u

        Now substitute uu back in:

        2x\sqrt{2 x}

      So, the result is: 32x3 \sqrt{2} \sqrt{x}

    The result is: 32x−5x3 \sqrt{2} \sqrt{x} - 5 x

  2. Add the constant of integration:

    32x−5x+constant3 \sqrt{2} \sqrt{x} - 5 x+ \mathrm{constant}

The answer is:

32x−5x+constant3 \sqrt{2} \sqrt{x} - 5 x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                          
 |                                           
 | /   3       \                    ___   ___
 | |------- - 5| dx = C - 5*x + 3*\/ 2 *\/ x 
 | |  _____    |                             
 | \\/ 2*x     /                             
 |                                           
/
∫(−5+32x) dx=C+32x−5x\int \left(-5 + \frac{3}{\sqrt{2 x}}\right)\, dx = C + 3 \sqrt{2} \sqrt{x} - 5 x
Simplify
The graph
3.07.03.54.04.55.05.56.06.50-40
Plot the graph f(x)
The answer [src] 
         ___
-5 + 3*\/ 2
−5+32-5 + 3 \sqrt{2} 
=
= 
         ___
-5 + 3*\/ 2
−5+32-5 + 3 \sqrt{2} 
-5 + 3*sqrt(2)
Numerical answer [src] 
-0.757359314006251
-0.757359314006251

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

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