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x*sqrt(1+5x^2)
Solving integrals/ x*sqrt(1+5x^2)

Integral of x*sqrt(1+5x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___                  
 \/ 7                   
   /                    
  |                     
  |        __________   
  |       /        2    
  |   x*\/  1 + 5*x   dx
  |                     
 /                      
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\/ 3
$$\int\limits_{\sqrt{3}}^{\sqrt{7}} x \sqrt{5 x^{2} + 1}\, dx$$ 
Integral(x*sqrt(1 + 5*x^2), (x, sqrt(3), sqrt(7)))
Detail solution

  1. Rewrite the integrand:

    SqrtQuadraticDenomRule(a=1, b=0, c=5, coeffs=[5, 0, 1, 0], context=(5*x**3 + x)/sqrt(5*x**2 + 1), symbol=x)

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                
 |                                                 
 |      __________             __________ /      2\
 |     /        2             /        2  |1    x |
 | x*\/  1 + 5*x   dx = C + \/  1 + 5*x  *|-- + --|
 |                                        \15   3 /
/
$$\int x \sqrt{5 x^{2} + 1}\, dx = C + \left(\frac{x^{2}}{3} + \frac{1}{15}\right) \sqrt{5 x^{2} + 1}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
152
---
 15
$$\frac{152}{15}$$ 
=
= 
152
---
 15
$$\frac{152}{15}$$
Упростить
Numerical answer [src] 
10.1333333333333
10.1333333333333
The graph
Integral of x*sqrt(1+5x^2) dx

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

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