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  • Identical expressions

  • one /((x^ two + nine)*sqrt(x^ two + sixteen))
  • 1 divide by ((x squared plus 9) multiply by square root of (x squared plus 16))
  • one divide by ((x to the power of two plus nine) multiply by square root of (x to the power of two plus sixteen))
  • 1/((x^2+9)*√(x^2+16))
  • 1/((x2+9)*sqrt(x2+16))
  • 1/x2+9*sqrtx2+16
  • 1/((x²+9)*sqrt(x²+16))
  • 1/((x to the power of 2+9)*sqrt(x to the power of 2+16))
  • 1/((x^2+9)sqrt(x^2+16))
  • 1/((x2+9)sqrt(x2+16))
  • 1/x2+9sqrtx2+16
  • 1/x^2+9sqrtx^2+16
  • 1 divide by ((x^2+9)*sqrt(x^2+16))
  • 1/((x^2+9)*sqrt(x^2+16))dx

  • Similar expressions

  • 1/((x^2+9)*sqrt(x^2-16))
  • 1/((x^2-9)*sqrt(x^2+16))
Solving integrals/ 1/((x^2+9)*sqrt(x^2+16))

Integral of 1/((x^2+9)*sqrt(x^2+16)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                         
  /                         
 |                          
 |            1             
 |  --------------------- dx
 |              _________   
 |  / 2    \   /  2         
 |  \x  + 9/*\/  x  + 16    
 |                          
/                           
-oo
$$\int\limits_{-\infty}^{\infty} \frac{1}{\left(x^{2} + 9\right) \sqrt{x^{2} + 16}}\, dx$$ 
Integral(1/((x^2 + 9)*sqrt(x^2 + 16)), (x, -oo, oo))
The answer (Indefinite) [src] 
  /                                 /                        
 |                                 |                         
 |           1                     |           1             
 | --------------------- dx = C +  | --------------------- dx
 |             _________           |             _________   
 | / 2    \   /  2                 | /     2\   /       2    
 | \x  + 9/*\/  x  + 16            | \9 + x /*\/  16 + x     
 |                                 |                         
/                                 /
$$\int \frac{1}{\left(x^{2} + 9\right) \sqrt{x^{2} + 16}}\, dx = C + \int \frac{1}{\left(x^{2} + 9\right) \sqrt{x^{2} + 16}}\, dx$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___   3/2       ___   ____          
4*\/ 7 *pi      8*\/ 7 *\/ pi *asin(3/4)
------------- - ------------------------
      7                    7            
----------------------------------------
                    ____                
               12*\/ pi
$$\frac{- \frac{8 \sqrt{7} \sqrt{\pi} \operatorname{asin}{\left(\frac{3}{4} \right)}}{7} + \frac{4 \sqrt{7} \pi^{\frac{3}{2}}}{7}}{12 \sqrt{\pi}}$$ 
=
= 
    ___   3/2       ___   ____          
4*\/ 7 *pi      8*\/ 7 *\/ pi *asin(3/4)
------------- - ------------------------
      7                    7            
----------------------------------------
                    ____                
               12*\/ pi
$$\frac{- \frac{8 \sqrt{7} \sqrt{\pi} \operatorname{asin}{\left(\frac{3}{4} \right)}}{7} + \frac{4 \sqrt{7} \pi^{\frac{3}{2}}}{7}}{12 \sqrt{\pi}}$$ 
(4*sqrt(7)*pi^(3/2)/7 - 8*sqrt(7)*sqrt(pi)*asin(3/4)/7)/(12*sqrt(pi))
Numerical answer [src] 
0.182111912733679
0.182111912733679

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

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