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Integral of x+1 dx

Limits of integration:

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The solution

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∫01(x+1) dx\int\limits_{0}^{1} \left(x + 1\right)\, dx 
Integral(x + 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

    The result is: x22+x\frac{x^{2}}{2} + x

  2. Now simplify:

    x(x+2)2\frac{x \left(x + 2\right)}{2}

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(x+1) dx=C+x22+x\int \left(x + 1\right)\, dx = C + \frac{x^{2}}{2} + x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
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32\frac{3}{2} 
=
= 
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32\frac{3}{2} 
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Numerical answer [src] 
1.5
1.5
The graph
Integral of x+1 dx

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

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