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Solving integrals/ 1/sqrt(10-3x)

Integral of 1/sqrt(10-3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3                
  /                
 |                 
 |       1         
 |  ------------ dx
 |    __________   
 |  \/ 10 - 3*x    
 |                 
/                  
1/3
$$\int\limits_{\frac{1}{3}}^{3} \frac{1}{\sqrt{10 - 3 x}}\, dx$$ 
Integral(1/(sqrt(10 - 3*x)), (x, 1/3, 3))
Detail solution

  1. Let .

    Then let and substitute :

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

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

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
 |                           __________
 |      1                2*\/ 10 - 3*x 
 | ------------ dx = C - --------------
 |   __________                3       
 | \/ 10 - 3*x                         
 |                                     
/
$$\int \frac{1}{\sqrt{10 - 3 x}}\, dx = C - \frac{2 \sqrt{10 - 3 x}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
4/3
$$\frac{4}{3}$$ 
=
= 
4/3
$$\frac{4}{3}$$ 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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