Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of xsqrt(x²+1)
Integral of (x+3)/(x^2-5x+6)
Integral of exp(-cos(x))*sin(x)
Integral of e^((-x)^2)*x*dx
Identical expressions
sqrt(lnx)/x^ two
square root of (lnx) divide by x squared
square root of (lnx) divide by x to the power of two
√(lnx)/x^2
sqrt(lnx)/x2
sqrtlnx/x2
sqrt(lnx)/x²
sqrt(lnx)/x to the power of 2
sqrtlnx/x^2
sqrt(lnx) divide by x^2
sqrt(lnx)/x^2dx

Integral of sqrt(lnx)/x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \log{\left(x \right)}$ .

Then let $du = \frac{dx}{x}$ and substitute $du$ :

$\int \sqrt{u} e^{- u}\, du$
Now substitute $u$ back in:

$- \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{\log{\left(x \right)}} \right)}}{2} - \frac{\sqrt{\log{\left(x \right)}}}{x}$
Add the constant of integration:

$- \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{\log{\left(x \right)}} \right)}}{2} - \frac{\sqrt{\log{\left(x \right)}}}{x}+ \mathrm{constant}$

The answer is:

$- \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{\log{\left(x \right)}} \right)}}{2} - \frac{\sqrt{\log{\left(x \right)}}}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                                         
 |   ________            ________     ____     /  ________\
 | \/ log(x)           \/ log(x)    \/ pi *erfc\\/ log(x) /
 | ---------- dx = C - ---------- - -----------------------
 |      2                  x                   2           
 |     x                                                   
 |                                                         
/

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

Simplify

The answer [src]

         ____
       \/ pi 
oo*I - ------
         2

$$- \frac{\sqrt{\pi}}{2} + \infty i$$

         ____
       \/ pi 
oo*I - ------
         2

$$- \frac{\sqrt{\pi}}{2} + \infty i$$

oo*i - sqrt(pi)/2

Numerical answer [src]

(0.0 + 9.0496069992061e+19j)

(0.0 + 9.0496069992061e+19j)

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

Other calculators

How to use it?

Identical expressions

Integral of sqrt(lnx)/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution