3.44.82 \(\int \frac {1}{25} (340-2724 x-2580 x^2+7396 x^3+e^{10} (-100+860 x)) \, dx\) [4382]

Optimal. Leaf size=28 \[ \left (4-e^{10}+2 x-9 x^2+\frac {1}{5} \left (-3+2 x^2\right )\right )^2 \]

[Out]

(17/5+2*x-43/5*x^2-exp(5)^2)^2

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Rubi [A]
time = 0.01, antiderivative size = 41, normalized size of antiderivative = 1.46, number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12} \begin {gather*} \frac {1849 x^4}{25}-\frac {172 x^3}{5}-\frac {1362 x^2}{25}+\frac {68 x}{5}+\frac {2}{215} e^{10} (5-43 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(340 - 2724*x - 2580*x^2 + 7396*x^3 + E^10*(-100 + 860*x))/25,x]

[Out]

(2*E^10*(5 - 43*x)^2)/215 + (68*x)/5 - (1362*x^2)/25 - (172*x^3)/5 + (1849*x^4)/25

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \left (340-2724 x-2580 x^2+7396 x^3+e^{10} (-100+860 x)\right ) \, dx\\ &=\frac {2}{215} e^{10} (5-43 x)^2+\frac {68 x}{5}-\frac {1362 x^2}{25}-\frac {172 x^3}{5}+\frac {1849 x^4}{25}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 43, normalized size = 1.54 \begin {gather*} \frac {4}{25} \left (85 x-25 e^{10} x-\frac {681 x^2}{2}+\frac {215 e^{10} x^2}{2}-215 x^3+\frac {1849 x^4}{4}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(340 - 2724*x - 2580*x^2 + 7396*x^3 + E^10*(-100 + 860*x))/25,x]

[Out]

(4*(85*x - 25*E^10*x - (681*x^2)/2 + (215*E^10*x^2)/2 - 215*x^3 + (1849*x^4)/4))/25

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Maple [A]
time = 0.43, size = 21, normalized size = 0.75

method	result	size
default	\(\frac {\left (5 \,{\mathrm e}^{10}+43 x^{2}-10 x -17\right )^{2}}{25}\)	\(21\)
gosper	\(\frac {x \left (430 x \,{\mathrm e}^{10}+1849 x^{3}-100 \,{\mathrm e}^{10}-860 x^{2}-1362 x +340\right )}{25}\)	\(32\)
risch	\(\frac {86 \,{\mathrm e}^{10} x^{2}}{5}-4 x \,{\mathrm e}^{10}+\frac {1849 x^{4}}{25}-\frac {172 x^{3}}{5}-\frac {1362 x^{2}}{25}+\frac {68 x}{5}\)	\(32\)
norman	\(\left (-4 \,{\mathrm e}^{10}+\frac {68}{5}\right ) x +\left (\frac {86 \,{\mathrm e}^{10}}{5}-\frac {1362}{25}\right ) x^{2}-\frac {172 x^{3}}{5}+\frac {1849 x^{4}}{25}\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*(860*x-100)*exp(5)^2+7396/25*x^3-516/5*x^2-2724/25*x+68/5,x,method=_RETURNVERBOSE)

[Out]

1/25*(5*exp(5)^2+43*x^2-10*x-17)^2

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Maxima [A]
time = 0.28, size = 32, normalized size = 1.14 \begin {gather*} \frac {1849}{25} \, x^{4} - \frac {172}{5} \, x^{3} - \frac {1362}{25} \, x^{2} + \frac {2}{5} \, {\left (43 \, x^{2} - 10 \, x\right )} e^{10} + \frac {68}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(860*x-100)*exp(5)^2+7396/25*x^3-516/5*x^2-2724/25*x+68/5,x, algorithm="maxima")

[Out]

1849/25*x^4 - 172/5*x^3 - 1362/25*x^2 + 2/5*(43*x^2 - 10*x)*e^10 + 68/5*x

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Fricas [A]
time = 0.39, size = 32, normalized size = 1.14 \begin {gather*} \frac {1849}{25} \, x^{4} - \frac {172}{5} \, x^{3} - \frac {1362}{25} \, x^{2} + \frac {2}{5} \, {\left (43 \, x^{2} - 10 \, x\right )} e^{10} + \frac {68}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(860*x-100)*exp(5)^2+7396/25*x^3-516/5*x^2-2724/25*x+68/5,x, algorithm="fricas")

[Out]

1849/25*x^4 - 172/5*x^3 - 1362/25*x^2 + 2/5*(43*x^2 - 10*x)*e^10 + 68/5*x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 36 vs. \(2 (17) = 34\).
time = 0.01, size = 36, normalized size = 1.29 \begin {gather*} \frac {1849 x^{4}}{25} - \frac {172 x^{3}}{5} + x^{2} \left (- \frac {1362}{25} + \frac {86 e^{10}}{5}\right ) + x \left (\frac {68}{5} - 4 e^{10}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(860*x-100)*exp(5)**2+7396/25*x**3-516/5*x**2-2724/25*x+68/5,x)

[Out]

1849*x**4/25 - 172*x**3/5 + x**2*(-1362/25 + 86*exp(10)/5) + x*(68/5 - 4*exp(10))

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Giac [A]
time = 0.43, size = 32, normalized size = 1.14 \begin {gather*} \frac {1849}{25} \, x^{4} - \frac {172}{5} \, x^{3} - \frac {1362}{25} \, x^{2} + \frac {2}{5} \, {\left (43 \, x^{2} - 10 \, x\right )} e^{10} + \frac {68}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(860*x-100)*exp(5)^2+7396/25*x^3-516/5*x^2-2724/25*x+68/5,x, algorithm="giac")

[Out]

1849/25*x^4 - 172/5*x^3 - 1362/25*x^2 + 2/5*(43*x^2 - 10*x)*e^10 + 68/5*x

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Mupad [B]
time = 3.03, size = 30, normalized size = 1.07 \begin {gather*} \frac {1849\,x^4}{25}-\frac {172\,x^3}{5}+\left (\frac {86\,{\mathrm {e}}^{10}}{5}-\frac {1362}{25}\right )\,x^2+\left (\frac {68}{5}-4\,{\mathrm {e}}^{10}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((7396*x^3)/25 - (516*x^2)/5 - (2724*x)/25 + (exp(10)*(860*x - 100))/25 + 68/5,x)

[Out]

x^2*((86*exp(10))/5 - 1362/25) - (172*x^3)/5 + (1849*x^4)/25 - x*(4*exp(10) - 68/5)

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