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sqrt(1+sqrt(x))
Solving integrals/ sqrt(1+sqrt(x))

Integral of sqrt(1+sqrt(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
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 |  \/  1 + \/ x   dx
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0
$$\int\limits_{0}^{1} \sqrt{\sqrt{x} + 1}\, dx$$ 
Integral(sqrt(1 + sqrt(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                                                                       
 |                                                                     ___________             ___________              ___________            ___________
 |    ___________                   2                5/2          2   /       ___       5/2   /       ___        7/2   /       ___        3   /       ___ 
 |   /       ___                 8*x              8*x          8*x *\/  1 + \/ x     4*x   *\/  1 + \/ x     12*x   *\/  1 + \/ x     16*x *\/  1 + \/ x  
 | \/  1 + \/ x   dx = C + --------------- + --------------- - ------------------- - --------------------- + ---------------------- + --------------------
 |                             2       5/2       2       5/2         2       5/2            2       5/2             2       5/2             2       5/2   
/                          15*x  + 15*x      15*x  + 15*x        15*x  + 15*x           15*x  + 15*x            15*x  + 15*x            15*x  + 15*x
$$\int \sqrt{\sqrt{x} + 1}\, dx = C + \frac{12 x^{\frac{7}{2}} \sqrt{\sqrt{x} + 1}}{15 x^{\frac{5}{2}} + 15 x^{2}} - \frac{4 x^{\frac{5}{2}} \sqrt{\sqrt{x} + 1}}{15 x^{\frac{5}{2}} + 15 x^{2}} + \frac{8 x^{\frac{5}{2}}}{15 x^{\frac{5}{2}} + 15 x^{2}} + \frac{16 x^{3} \sqrt{\sqrt{x} + 1}}{15 x^{\frac{5}{2}} + 15 x^{2}} - \frac{8 x^{2} \sqrt{\sqrt{x} + 1}}{15 x^{\frac{5}{2}} + 15 x^{2}} + \frac{8 x^{2}}{15 x^{\frac{5}{2}} + 15 x^{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         ___
8    8*\/ 2 
-- + -------
15      15
$$\frac{8}{15} + \frac{8 \sqrt{2}}{15}$$ 
=
= 
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8    8*\/ 2 
-- + -------
15      15
$$\frac{8}{15} + \frac{8 \sqrt{2}}{15}$$ 
8/15 + 8*sqrt(2)/15
Numerical answer [src] 
1.28758056659898
1.28758056659898
The graph
Integral of sqrt(1+sqrt(x)) dx

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

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