Mister Exam

Other calculators

Solving integrals/ 1/(xsqrt(x^2-9))

Integral of 1/(xsqrt(x^2-9)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |       ________   
 |      /  2        
 |  x*\/  x  - 9    
 |                  
/                   
0
∫011xx2−9 dx\int\limits_{0}^{1} \frac{1}{x \sqrt{x^{2} - 9}}\, dx 
Integral(1/(x*sqrt(x^2 - 9)), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=3*sec(_theta), rewritten=1/3, substep=ConstantRule(constant=1/3, context=1/3, symbol=_theta), restriction=(x > -3) & (x < 3), context=1/(x*sqrt(x**2 - 9)), symbol=x)

  1. Add the constant of integration:

    {acos⁡(3x)3for x>−3∧x<3+constant\begin{cases} \frac{\operatorname{acos}{\left(\frac{3}{x} \right)}}{3} & \text{for}\: x > -3 \wedge x < 3 \end{cases}+ \mathrm{constant}

The answer is:

{acos⁡(3x)3for x>−3∧x<3+constant\begin{cases} \frac{\operatorname{acos}{\left(\frac{3}{x} \right)}}{3} & \text{for}\: x > -3 \wedge x < 3 \end{cases}+ \mathrm{constant}

The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
Plot the graph f(x)
The answer [src] 
        I*acosh(3)
-oo*I + ----------
            3
−∞i+iacosh⁡(3)3- \infty i + \frac{i \operatorname{acosh}{\left(3 \right)}}{3} 
=
= 
        I*acosh(3)
-oo*I + ----------
            3
−∞i+iacosh⁡(3)3- \infty i + \frac{i \operatorname{acosh}{\left(3 \right)}}{3} 
-oo*i + i*acosh(3)/3
Numerical answer [src] 
(0.0 - 14.7064861430606j)
(0.0 - 14.7064861430606j)

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

    © Mister Exam – Calculator