Integral of x+cosx dx

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

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of cosine is sine:
  
  $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
The result is: $\frac{x^{2}}{2} + \sin{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                       2         
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 | (x + cos(x)) dx = C + -- + sin(x)
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$$\int \left(x + \cos{\left(x \right)}\right)\, dx = C + \frac{x^{2}}{2} + \sin{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2 + sin(1)

$$\frac{1}{2} + \sin{\left(1 \right)}$$

1/2 + sin(1)

$$\frac{1}{2} + \sin{\left(1 \right)}$$

1/2 + sin(1)

Numerical answer [src]

1.3414709848079

1.3414709848079

The graph

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