3.43.34 \(\int (-51-250 x-300 x^2-400 x^3) \, dx\)

Optimal. Leaf size=29 \[ \frac {1}{e}-x-\left (5-x^2+x (x+5 (1+2 x))\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 19, normalized size of antiderivative = 0.66, 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*} -100 x^4-100 x^3-125 x^2-51 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-51 - 250*x - 300*x^2 - 400*x^3,x]

[Out]

-51*x - 125*x^2 - 100*x^3 - 100*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-51 x-125 x^2-100 x^3-100 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.66 \begin {gather*} -51 x-125 x^2-100 x^3-100 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-51 - 250*x - 300*x^2 - 400*x^3,x]

[Out]

-51*x - 125*x^2 - 100*x^3 - 100*x^4

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fricas [A]  time = 0.47, size = 19, normalized size = 0.66 \begin {gather*} -100 \, x^{4} - 100 \, x^{3} - 125 \, x^{2} - 51 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-400*x^3-300*x^2-250*x-51,x, algorithm="fricas")

[Out]

-100*x^4 - 100*x^3 - 125*x^2 - 51*x

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giac [A]  time = 0.15, size = 19, normalized size = 0.66 \begin {gather*} -100 \, x^{4} - 100 \, x^{3} - 125 \, x^{2} - 51 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-400*x^3-300*x^2-250*x-51,x, algorithm="giac")

[Out]

-100*x^4 - 100*x^3 - 125*x^2 - 51*x

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maple [A]  time = 0.01, size = 19, normalized size = 0.66

method	result	size
gosper	\(-x \left (100 x^{3}+100 x^{2}+125 x +51\right )\)	\(19\)
default	\(-100 x^{4}-100 x^{3}-125 x^{2}-51 x\)	\(20\)
norman	\(-100 x^{4}-100 x^{3}-125 x^{2}-51 x\)	\(20\)
risch	\(-100 x^{4}-100 x^{3}-125 x^{2}-51 x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-400*x^3-300*x^2-250*x-51,x,method=_RETURNVERBOSE)

[Out]

-x*(100*x^3+100*x^2+125*x+51)

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maxima [A]  time = 0.34, size = 19, normalized size = 0.66 \begin {gather*} -100 \, x^{4} - 100 \, x^{3} - 125 \, x^{2} - 51 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-400*x^3-300*x^2-250*x-51,x, algorithm="maxima")

[Out]

-100*x^4 - 100*x^3 - 125*x^2 - 51*x

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mupad [B]  time = 0.03, size = 19, normalized size = 0.66 \begin {gather*} -100\,x^4-100\,x^3-125\,x^2-51\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 250*x - 300*x^2 - 400*x^3 - 51,x)

[Out]

- 51*x - 125*x^2 - 100*x^3 - 100*x^4

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sympy [A]  time = 0.05, size = 19, normalized size = 0.66 \begin {gather*} - 100 x^{4} - 100 x^{3} - 125 x^{2} - 51 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-400*x**3-300*x**2-250*x-51,x)

[Out]

-100*x**4 - 100*x**3 - 125*x**2 - 51*x

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