Integral of x-3/2x^2+5x-7 dx
The solution
Detail solution
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Integrate term-by-term:
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
∫5xdx=5∫xdx
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
So, the result is: 25x2
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
∫(−23x2)dx=−23∫x2dx
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The integral of xn is n+1xn+1 when n=−1:
∫x2dx=3x3
So, the result is: −2x3
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
The result is: −2x3+2x2
The result is: −2x3+3x2
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The integral of a constant is the constant times the variable of integration:
∫(−7)dx=−7x
The result is: −2x3+3x2−7x
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Now simplify:
2x(−x2+6x−14)
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Add the constant of integration:
2x(−x2+6x−14)+constant
The answer is:
2x(−x2+6x−14)+constant
The answer (Indefinite)
[src]
/
|
| / 2 \ 3
| | 3*x | 2 x
| |x - ---- + 5*x - 7| dx = C - 7*x + 3*x - --
| \ 2 / 2
|
/
∫((5x+(−23x2+x))−7)dx=C−2x3+3x2−7x
The graph
Use the examples entering the upper and lower limits of integration.