Integral of x(x-1)(x-2) dx
The solution
Detail solution
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Rewrite the integrand:
x(x−1)(x−2)=x3−3x2+2x
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Integrate term-by-term:
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The integral of xn is n+1xn+1 when n=−1:
∫x3dx=4x4
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The integral of a constant times a function is the constant times the integral of the function:
∫(−3x2)dx=−3∫x2dx
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The integral of xn is n+1xn+1 when n=−1:
∫x2dx=3x3
So, the result is: −x3
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The integral of a constant times a function is the constant times the integral of the function:
∫2xdx=2∫xdx
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
So, the result is: x2
The result is: 4x4−x3+x2
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Now simplify:
x2(4x2−x+1)
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Add the constant of integration:
x2(4x2−x+1)+constant
The answer is:
x2(4x2−x+1)+constant
The answer (Indefinite)
[src]
/ 4
| 2 3 x
| x*(x - 1)*(x - 2) dx = C + x - x + --
| 4
/
∫x(x−1)(x−2)dx=C+4x4−x3+x2
The graph
Use the examples entering the upper and lower limits of integration.