Integral of (sqrt2+x) dx

The solution

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-5

$$\int\limits_{-5}^{1} \left(x + \sqrt{2}\right)\, dx$$

Integral(sqrt(2) + x, (x, -5, 1))

Detail solution

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

$\frac{x \left(x + 2 \sqrt{2}\right)}{2}$
Add the constant of integration:

$\frac{x \left(x + 2 \sqrt{2}\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 2 \sqrt{2}\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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-12 + 6*\/ 2

$${{5\,2^{{{3}\over{2}}}-25}\over{2}}+{{2^{{{3}\over{2}}}+1}\over{2}}$$

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-12 + 6*\/ 2

$$-12 + 6 \sqrt{2}$$

Упростить

Numerical answer [src]

-3.51471862576143

-3.51471862576143

The graph

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

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Integral of (sqrt2+x) dx

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The solution