3.31.56 \(\int (1373-588 x+84 x^2-4 x^3) \, dx\)

Optimal. Leaf size=15 \[ 22+e^5-(7-x)^4+x \]

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Rubi [A]  time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^4+28 x^3-294 x^2+1373 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1373 - 588*x + 84*x^2 - 4*x^3,x]

[Out]

1373*x - 294*x^2 + 28*x^3 - x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=1373 x-294 x^2+28 x^3-x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.27 \begin {gather*} 1373 x-294 x^2+28 x^3-x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1373 - 588*x + 84*x^2 - 4*x^3,x]

[Out]

1373*x - 294*x^2 + 28*x^3 - x^4

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fricas [A]  time = 0.66, size = 19, normalized size = 1.27 \begin {gather*} -x^{4} + 28 \, x^{3} - 294 \, x^{2} + 1373 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+84*x^2-588*x+1373,x, algorithm="fricas")

[Out]

-x^4 + 28*x^3 - 294*x^2 + 1373*x

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giac [A]  time = 0.15, size = 19, normalized size = 1.27 \begin {gather*} -x^{4} + 28 \, x^{3} - 294 \, x^{2} + 1373 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+84*x^2-588*x+1373,x, algorithm="giac")

[Out]

-x^4 + 28*x^3 - 294*x^2 + 1373*x

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maple [A]  time = 0.02, size = 17, normalized size = 1.13

method	result	size
gosper	\(-x \left (x^{3}-28 x^{2}+294 x -1373\right )\)	\(17\)
default	\(-x^{4}+28 x^{3}-294 x^{2}+1373 x\)	\(20\)
norman	\(-x^{4}+28 x^{3}-294 x^{2}+1373 x\)	\(20\)
risch	\(-x^{4}+28 x^{3}-294 x^{2}+1373 x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*x^3+84*x^2-588*x+1373,x,method=_RETURNVERBOSE)

[Out]

-x*(x^3-28*x^2+294*x-1373)

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maxima [A]  time = 0.39, size = 19, normalized size = 1.27 \begin {gather*} -x^{4} + 28 \, x^{3} - 294 \, x^{2} + 1373 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x^3+84*x^2-588*x+1373,x, algorithm="maxima")

[Out]

-x^4 + 28*x^3 - 294*x^2 + 1373*x

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mupad [B]  time = 0.03, size = 19, normalized size = 1.27 \begin {gather*} -x^4+28\,x^3-294\,x^2+1373\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(84*x^2 - 588*x - 4*x^3 + 1373,x)

[Out]

1373*x - 294*x^2 + 28*x^3 - x^4

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sympy [A]  time = 0.05, size = 15, normalized size = 1.00 \begin {gather*} - x^{4} + 28 x^{3} - 294 x^{2} + 1373 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*x**3+84*x**2-588*x+1373,x)

[Out]

-x**4 + 28*x**3 - 294*x**2 + 1373*x

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