Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^3/(x^2+1)^2
Integral of e^(-x)*sin(2*x)
Integral of ln(cosx)
Integral of dx/((2*x))
Identical expressions
(3x- seven)/(sqrt(x^ two -5x+ one))
(3x minus 7) divide by ( square root of (x squared minus 5x plus 1))
(3x minus seven) divide by ( square root of (x to the power of two minus 5x plus one))
(3x-7)/(√(x^2-5x+1))
(3x-7)/(sqrt(x2-5x+1))
3x-7/sqrtx2-5x+1
(3x-7)/(sqrt(x²-5x+1))
(3x-7)/(sqrt(x to the power of 2-5x+1))
3x-7/sqrtx^2-5x+1
(3x-7) divide by (sqrt(x^2-5x+1))
(3x-7)/(sqrt(x^2-5x+1))dx
Similar expressions
(3x+7)/(sqrt(x^2-5x+1))
(3x-7)/(sqrt(x^2+5x+1))
(3x-7)/(sqrt(x^2-5x-1))

Solving integrals/ (3x-7)/(sqrt(x^2-5x+1))

Integral of (3x-7)/(sqrt(x^2-5x+1)) dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |       3*x - 7        
 |  ----------------- dx
 |     ______________   
 |    /  2              
 |  \/  x  - 5*x + 1    
 |                      
/                       
0

$$\int\limits_{0}^{1} \frac{3 x - 7}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$$

Integral((3*x - 7)/sqrt(x^2 - 5*x + 1), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{3 x - 7}{\sqrt{\left(x^{2} - 5 x\right) + 1}} = \frac{3 x}{\sqrt{\left(x^{2} - 5 x\right) + 1}} - \frac{7}{\sqrt{\left(x^{2} - 5 x\right) + 1}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3 x}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx = 3 \int \frac{x}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx$
  So, the result is: $3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{7}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\right)\, dx = - 7 \int \frac{1}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \frac{1}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$
  So, the result is: $- 7 \int \frac{1}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$
The result is: $3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx - 7 \int \frac{1}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$
Now simplify:

$3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx - 7 \int \frac{1}{\sqrt{x^{2} - 5 x + 1}}\, dx$
Add the constant of integration:

$3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx - 7 \int \frac{1}{\sqrt{x^{2} - 5 x + 1}}\, dx+ \mathrm{constant}$

The answer is:

$3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx - 7 \int \frac{1}{\sqrt{x^{2} - 5 x + 1}}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               /                           /                    
 |                               |                           |                     
 |      3*x - 7                  |         1                 |         x           
 | ----------------- dx = C - 7* | ----------------- dx + 3* | ----------------- dx
 |    ______________             |    ______________         |    ______________   
 |   /  2                        |   /  2                    |   /      2          
 | \/  x  - 5*x + 1              | \/  x  - 5*x + 1          | \/  1 + x  - 5*x    
 |                               |                           |                     
/                               /                           /

$$\int \frac{3 x - 7}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx = C + 3 \int \frac{x}{\sqrt{x^{2} - 5 x + 1}}\, dx - 7 \int \frac{1}{\sqrt{\left(x^{2} - 5 x\right) + 1}}\, dx$$

Simplify

The answer [src]

  1                     
  /                     
 |                      
 |       -7 + 3*x       
 |  ----------------- dx
 |     ______________   
 |    /      2          
 |  \/  1 + x  - 5*x    
 |                      
/                       
0

$$\int\limits_{0}^{1} \frac{3 x - 7}{\sqrt{x^{2} - 5 x + 1}}\, dx$$

  1                     
  /                     
 |                      
 |       -7 + 3*x       
 |  ----------------- dx
 |     ______________   
 |    /      2          
 |  \/  1 + x  - 5*x    
 |                      
/                       
0

$$\int\limits_{0}^{1} \frac{3 x - 7}{\sqrt{x^{2} - 5 x + 1}}\, dx$$

Integral((-7 + 3*x)/sqrt(1 + x^2 - 5*x), (x, 0, 1))

Numerical answer [src]

(-2.55521669473954 + 4.67768686993639j)

(-2.55521669473954 + 4.67768686993639j)

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3x-7)/(sqrt(x^2-5x+1)) dx

Limits of integration:

The graph:

Piecewise:

The solution