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(2x+1)dx
Solving integrals/ (2x+1)dx

Integral of (2x+1)dx dx

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The solution

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∫01(2x+1) dx\int\limits_{0}^{1} \left(2 x + 1\right)\, dx 
Integral(2*x + 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫2x dx=2∫x dx\int 2 x\, dx = 2 \int x\, dx

      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}

      So, the result is: x2x^{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: x2+xx^{2} + x

  2. Now simplify:

    x(x+1)x \left(x + 1\right)

  3. Add the constant of integration:

    x(x+1)+constantx \left(x + 1\right)+ \mathrm{constant}

The answer is:

x(x+1)+constantx \left(x + 1\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(2x+1) dx=C+x2+x\int \left(2 x + 1\right)\, dx = C + x^{2} + x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
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22 
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Numerical answer [src] 
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The graph
Integral of (2x+1)dx dx

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

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