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3x^2-5
Solving integrals/ 3x^2-5

Integral of 3x^2-5 dx

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The solution

You have entered [src] 
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∫01(3x2−5) dx\int\limits_{0}^{1} \left(3 x^{2} - 5\right)\, dx 
Integral(3*x^2 - 1*5, (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:

      ∫3x2 dx=3∫x2 dx\int 3 x^{2}\, dx = 3 \int x^{2}\, dx

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

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: x3x^{3}

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

      ∫((−1)5) dx=−5x\int \left(\left(-1\right) 5\right)\, dx = - 5 x

    The result is: x3−5xx^{3} - 5 x

  2. Now simplify:

    x(x2−5)x \left(x^{2} - 5\right)

  3. Add the constant of integration:

    x(x2−5)+constantx \left(x^{2} - 5\right)+ \mathrm{constant}

The answer is:

x(x2−5)+constantx \left(x^{2} - 5\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
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 | \3*x  - 5/ dx = C + x  - 5*x
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x3−5 xx^3-5\,x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-10
Plot the graph f(x)
The answer [src] 
-4
−4-4 
=
= 
-4
−4-4
Simplify
Numerical answer [src] 
-4.0
-4.0
The graph
Integral of 3x^2-5 dx

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

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