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x+6
Solving integrals/ x+6

Integral of x+6 dx

Limits of integration:

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The solution

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∫01(x+6) dx\int\limits_{0}^{1} \left(x + 6\right)\, dx 
Integral(x + 6, (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:

      ∫6 dx=6x\int 6\, dx = 6 x

    The result is: x22+6x\frac{x^{2}}{2} + 6 x

  2. Now simplify:

    x(x+12)2\frac{x \left(x + 12\right)}{2}

  3. Add the constant of integration:

    x(x+12)2+constant\frac{x \left(x + 12\right)}{2}+ \mathrm{constant}

The answer is:

x(x+12)2+constant\frac{x \left(x + 12\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x+6) dx=C+x22+6x\int \left(x + 6\right)\, dx = C + \frac{x^{2}}{2} + 6 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
13/2
132\frac{13}{2} 
=
= 
13/2
132\frac{13}{2} 
13/2
Numerical answer [src] 
6.5
6.5
The graph
Integral of x+6 dx

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

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