3.47.75 \(\int (-3272+32 x-640 \log (5)-32 \log ^2(5)) \, dx\) [4675]

Optimal. Leaf size=19 \[ \left (9+\log \left (e^{-4 x+4 (10+\log (5))^2}\right )\right )^2 \]

[Out]

(ln(exp((10+ln(5))^2-x)^4)+9)^2

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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.11, 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*} 16 x^2-8 x \left (409+4 \log ^2(5)+80 \log (5)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3272 + 32*x - 640*Log[5] - 32*Log[5]^2,x]

[Out]

16*x^2 - 8*x*(409 + 80*Log[5] + 4*Log[5]^2)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=16 x^2-8 x \left (409+80 \log (5)+4 \log ^2(5)\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.11 \begin {gather*} -3272 x+16 x^2-640 x \log (5)-32 x \log ^2(5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3272 + 32*x - 640*Log[5] - 32*Log[5]^2,x]

[Out]

-3272*x + 16*x^2 - 640*x*Log[5] - 32*x*Log[5]^2

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Maple [A]
time = 0.23, size = 22, normalized size = 1.16

method	result	size
gosper	\(-8 x \left (4 \ln \left (5\right )^{2}+80 \ln \left (5\right )-2 x +409\right )\)	\(19\)
norman	\(\left (-32 \ln \left (5\right )^{2}-640 \ln \left (5\right )-3272\right ) x +16 x^{2}\)	\(21\)
default	\(-32 x \ln \left (5\right )^{2}-640 x \ln \left (5\right )+16 x^{2}-3272 x\)	\(22\)
risch	\(-32 x \ln \left (5\right )^{2}-640 x \ln \left (5\right )+16 x^{2}-3272 x\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-32*ln(5)^2-640*ln(5)+32*x-3272,x,method=_RETURNVERBOSE)

[Out]

-32*x*ln(5)^2-640*x*ln(5)+16*x^2-3272*x

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Maxima [A]
time = 0.30, size = 21, normalized size = 1.11 \begin {gather*} -32 \, x \log \left (5\right )^{2} + 16 \, x^{2} - 640 \, x \log \left (5\right ) - 3272 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(5)^2-640*log(5)+32*x-3272,x, algorithm="maxima")

[Out]

-32*x*log(5)^2 + 16*x^2 - 640*x*log(5) - 3272*x

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Fricas [A]
time = 0.34, size = 21, normalized size = 1.11 \begin {gather*} -32 \, x \log \left (5\right )^{2} + 16 \, x^{2} - 640 \, x \log \left (5\right ) - 3272 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(5)^2-640*log(5)+32*x-3272,x, algorithm="fricas")

[Out]

-32*x*log(5)^2 + 16*x^2 - 640*x*log(5) - 3272*x

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Sympy [A]
time = 0.01, size = 20, normalized size = 1.05 \begin {gather*} 16 x^{2} + x \left (-3272 - 640 \log {\left (5 \right )} - 32 \log {\left (5 \right )}^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*ln(5)**2-640*ln(5)+32*x-3272,x)

[Out]

16*x**2 + x*(-3272 - 640*log(5) - 32*log(5)**2)

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Giac [A]
time = 0.40, size = 21, normalized size = 1.11 \begin {gather*} -32 \, x \log \left (5\right )^{2} + 16 \, x^{2} - 640 \, x \log \left (5\right ) - 3272 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(5)^2-640*log(5)+32*x-3272,x, algorithm="giac")

[Out]

-32*x*log(5)^2 + 16*x^2 - 640*x*log(5) - 3272*x

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Mupad [B]
time = 0.04, size = 21, normalized size = 1.11 \begin {gather*} 16\,x^2-x\,\left (640\,\ln \left (5\right )+32\,{\ln \left (5\right )}^2+3272\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x - 640*log(5) - 32*log(5)^2 - 3272,x)

[Out]

16*x^2 - x*(640*log(5) + 32*log(5)^2 + 3272)

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