Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*e^(x*(-2))
Integral of 1/(2+3x^2)
Integral of x^2*e^2
Integral of x^0.5
Identical expressions
lnx/(one +x^ two)^(one / two)
lnx divide by (1 plus x squared ) to the power of (1 divide by 2)
lnx divide by (one plus x to the power of two) to the power of (one divide by two)
lnx/(1+x2)(1/2)
lnx/1+x21/2
lnx/(1+x²)^(1/2)
lnx/(1+x to the power of 2) to the power of (1/2)
lnx/1+x^2^1/2
lnx divide by (1+x^2)^(1 divide by 2)
lnx/(1+x^2)^(1/2)dx
Similar expressions
lnx/(1-x^2)^(1/2)

Integral of lnx/(1+x^2)^(1/2) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |     log(x)     
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 + x     
 |                
/                 
0

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

Integral(log(x)/sqrt(1 + x^2), (x, 0, 1))

Detail solution

Use integration by parts:

$\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$

Let $u{\left(x \right)} = \log{\left(x \right)}$ and let $\operatorname{dv}{\left(x \right)} = \frac{1}{\sqrt{x^{2} + 1}}$ .

Then $\operatorname{du}{\left(x \right)} = \frac{1}{x}$ .

To find $v{\left(x \right)}$ :
Now evaluate the sub-integral.
Don't know the steps in finding this integral.

But the integral is

$\int \frac{\operatorname{asinh}{\left(x \right)}}{x}\, dx$
Add the constant of integration:

$\log{\left(x \right)} \operatorname{asinh}{\left(x \right)} - \int \frac{\operatorname{asinh}{\left(x \right)}}{x}\, dx+ \mathrm{constant}$

The answer is:

$\log{\left(x \right)} \operatorname{asinh}{\left(x \right)} - \int \frac{\operatorname{asinh}{\left(x \right)}}{x}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       /                             
 |                       |                              
 |    log(x)             | asinh(x)                     
 | ----------- dx = C -  | -------- dx + asinh(x)*log(x)
 |    ________           |    x                         
 |   /      2            |                              
 | \/  1 + x            /                               
 |                                                      
/

$$\int \frac{\log{\left(x \right)}}{\sqrt{x^{2} + 1}}\, dx = C + \log{\left(x \right)} \operatorname{asinh}{\left(x \right)} - \int \frac{\operatorname{asinh}{\left(x \right)}}{x}\, dx$$

Simplify

The answer [src]

  1               
  /               
 |                
 |     log(x)     
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 + x     
 |                
/                 
0

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

  1               
  /               
 |                
 |     log(x)     
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 + x     
 |                
/                 
0

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

Integral(log(x)/sqrt(1 + x^2), (x, 0, 1))

Numerical answer [src]

-0.95520180648118

-0.95520180648118

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of lnx/(1+x^2)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution