Integral of sqrt1+sqrtx dx

The solution

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$$\int\limits_{0}^{1} \left(\sqrt{x} + \sqrt{1}\right)\, dx$$

Integral(sqrt(1) + sqrt(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \sqrt{1}\, dx = x$
The result is: $\frac{2 x^{\frac{3}{2}}}{3} + x$
Add the constant of integration:

$\frac{2 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}$

The answer is:

$\frac{2 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

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$${{2\,x^{{{3}\over{2}}}}\over{3}}+x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$${{5}\over{3}}$$

5/3

$$\frac{5}{3}$$

Упростить

Numerical answer [src]

1.66666666666667

1.66666666666667

The graph

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

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Integral of sqrt1+sqrtx dx

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The solution