Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2/(1+x^3)
Integral of √(1+x²)
Integral of x^2/sqrt(4-x^2)
Integral of a
Identical expressions
x/sqrt(two *x+ seven)
x divide by square root of (2 multiply by x plus 7)
x divide by square root of (two multiply by x plus seven)
x/√(2*x+7)
x/sqrt(2x+7)
x/sqrt2x+7
x divide by sqrt(2*x+7)
x/sqrt(2*x+7)dx
Similar expressions
(x)/sqrt(2x+7)
x/sqrt(2*x-7)
x/((sqrt2x+7))

Solving integrals/ x/sqrt(2*x+7)

Integral of x/sqrt(2*x+7) dx

The solution

You have entered [src]

  9               
  /               
 |                
 |       x        
 |  ----------- dx
 |    _________   
 |  \/ 2*x + 7    
 |                
/                 
1

$$\int\limits_{1}^{9} \frac{x}{\sqrt{2 x + 7}}\, dx$$

Integral(x/sqrt(2*x + 7), (x, 1, 9))

Detail solution

Let $u = \sqrt{2 x + 7}$ .

Then let $du = \frac{dx}{\sqrt{2 x + 7}}$ and substitute $du$ :

$\int \left(\frac{u^{2}}{2} - \frac{7}{2}\right)\, du$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u^{2}}{2}\, du = \frac{\int u^{2}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{2}\, du = \frac{u^{3}}{3}$
    So, the result is: $\frac{u^{3}}{6}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(- \frac{7}{2}\right)\, du = - \frac{7 u}{2}$
  The result is: $\frac{u^{3}}{6} - \frac{7 u}{2}$
Now substitute $u$ back in:

$\frac{\left(2 x + 7\right)^{\frac{3}{2}}}{6} - \frac{7 \sqrt{2 x + 7}}{2}$
Now simplify:

$\frac{\left(x - 7\right) \sqrt{2 x + 7}}{3}$
Add the constant of integration:

$\frac{\left(x - 7\right) \sqrt{2 x + 7}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\left(x - 7\right) \sqrt{2 x + 7}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                 
 |                          _________            3/2
 |      x               7*\/ 2*x + 7    (2*x + 7)   
 | ----------- dx = C - ------------- + ------------
 |   _________                2              6      
 | \/ 2*x + 7                                       
 |                                                  
/

$$\int \frac{x}{\sqrt{2 x + 7}}\, dx = C + \frac{\left(2 x + 7\right)^{\frac{3}{2}}}{6} - \frac{7 \sqrt{2 x + 7}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

28/3

$$\frac{28}{3}$$

28/3

$$\frac{28}{3}$$

28/3

Numerical answer [src]

9.33333333333333

9.33333333333333

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x/sqrt(2*x+7) dx

Limits of integration:

The graph:

Piecewise:

The solution