Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^3*dx
Integral of (1+4x^2)^(1/2)
Integral of x*e^(x^2+1)
Integral of x/(3x²-1)^4
Identical expressions
(one +4x^ two)^(one / two)
(1 plus 4x squared ) to the power of (1 divide by 2)
(one plus 4x to the power of two) to the power of (one divide by two)
(1+4x2)(1/2)
1+4x21/2
(1+4x²)^(1/2)
(1+4x to the power of 2) to the power of (1/2)
1+4x^2^1/2
(1+4x^2)^(1 divide by 2)
(1+4x^2)^(1/2)dx
Similar expressions
(1-4x^2)^(1/2)

Solving integrals/ (1+4x^2)^(1/2)

Integral of (1+4x^2)^(1/2) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  1 + 4*x   dx
 |                  
/                   
0

\int\limits_{0}^{1} \sqrt{4 x^{2} + 1}\, dx

Integral(sqrt(1 + 4*x^2), (x, 0, 1))

The answer (Indefinite) [src]

  /                                                   
 |                                          __________
 |    __________                           /        2 
 |   /        2           asinh(2*x)   x*\/  1 + 4*x  
 | \/  1 + 4*x   dx = C + ---------- + ---------------
 |                            4               2       
/

\int \sqrt{4 x^{2} + 1}\, dx = C + \frac{x \sqrt{4 x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(2 x \right)}}{4}

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ___           
\/ 5    asinh(2)
----- + --------
  2        4

\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}

  ___           
\/ 5    asinh(2)
----- + --------
  2        4

\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}

sqrt(5)/2 + asinh(2)/4

Numerical answer [src]

1.4789428575446

1.4789428575446

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (1+4x^2)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution