Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^3
Integral of (1-x^2)/(1+x^2)
Integral of 1/(x+1)^3
Integral of tan^(-1)x
Identical expressions
one /(sqrt9x^ two -6x+ ten)
1 divide by ( square root of 9x squared minus 6x plus 10)
one divide by ( square root of 9x to the power of two minus 6x plus ten)
1/(√9x^2-6x+10)
1/(sqrt9x2-6x+10)
1/sqrt9x2-6x+10
1/(sqrt9x²-6x+10)
1/(sqrt9x to the power of 2-6x+10)
1/sqrt9x^2-6x+10
1 divide by (sqrt9x^2-6x+10)
1/(sqrt9x^2-6x+10)dx
Similar expressions
1/(sqrt9x^2+6x+10)
1/(sqrt9x^2-6x-10)

Solving integrals/ 1/(sqrt9x^2-6x+10)

Integral of 1/(sqrt9x^2-6x+10) dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |             1            
 |  1*------------------- dx
 |           2              
 |      _____               
 |    \/ 9*x   - 6*x + 10   
 |                          
/                           
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{- 6 x + \left(\sqrt{9 x}\right)^{2} + 10}\, dx$$

Integral(1/((sqrt(9*x))^2 - 6*x + 10), (x, 0, 1))

Detail solution

Let $u = - 6 x + \left(\sqrt{9 x}\right)^{2} + 10$ .

Then let $du = \left(-6 + \frac{9 x}{x}\right) dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{9 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{3 u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\log{\left(- 6 x + \left(\sqrt{9 x}\right)^{2} + 10 \right)}}{3}$
Now simplify:

$\frac{\log{\left(3 x + 10 \right)}}{3}$
Add the constant of integration:

$\frac{\log{\left(3 x + 10 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(3 x + 10 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  /       2           \
 |                                   |  _____            |
 |            1                   log\\/ 9*x   - 6*x + 10/
 | 1*------------------- dx = C + ------------------------
 |          2                                3            
 |     _____                                              
 |   \/ 9*x   - 6*x + 10                                  
 |                                                        
/

$${{\log \left(3\,x+10\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  log(10)   log(13)
- ------- + -------
     3         3

$${{\log 13}\over{3}}-{{\log 10}\over{3}}$$

  log(10)   log(13)
- ------- + -------
     3         3

$$- \frac{\log{\left(10 \right)}}{3} + \frac{\log{\left(13 \right)}}{3}$$

Упростить

Numerical answer [src]

0.087454754822497

0.087454754822497

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 1/(sqrt9x^2-6x+10) dx

Limits of integration:

The graph:

Piecewise:

The solution