3.47.17 \(\int \frac {-7 e-14 x-60 \log (4)}{3 \log (4)} \, dx\)

Optimal. Leaf size=18 \[ 2-(e+x) \left (20+\frac {7 x}{3 \log (4)}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {9} \begin {gather*} -\frac {(14 x+7 e+60 \log (4))^2}{84 \log (4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-7*E - 14*x - 60*Log[4])/(3*Log[4]),x]

[Out]

-1/84*(7*E + 14*x + 60*Log[4])^2/Log[4]

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {(7 e+14 x+60 \log (4))^2}{84 \log (4)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 21, normalized size = 1.17 \begin {gather*} -\frac {7 e x+7 x^2+60 x \log (4)}{\log (64)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-7*E - 14*x - 60*Log[4])/(3*Log[4]),x]

[Out]

-((7*E*x + 7*x^2 + 60*x*Log[4])/Log[64])

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fricas [A]  time = 0.55, size = 22, normalized size = 1.22 \begin {gather*} -\frac {7 \, x^{2} + 7 \, x e + 120 \, x \log \relax (2)}{6 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(-120*log(2)-7*exp(1)-14*x)/log(2),x, algorithm="fricas")

[Out]

-1/6*(7*x^2 + 7*x*e + 120*x*log(2))/log(2)

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giac [A]  time = 0.14, size = 22, normalized size = 1.22 \begin {gather*} -\frac {7 \, x^{2} + 7 \, x e + 120 \, x \log \relax (2)}{6 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(-120*log(2)-7*exp(1)-14*x)/log(2),x, algorithm="giac")

[Out]

-1/6*(7*x^2 + 7*x*e + 120*x*log(2))/log(2)

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maple [A]  time = 0.03, size = 20, normalized size = 1.11

method	result	size
gosper	\(-\frac {x \left (7 x +7 \,{\mathrm e}+120 \ln \relax (2)\right )}{6 \ln \relax (2)}\)	\(20\)
default	\(\frac {-120 x \ln \relax (2)-7 x \,{\mathrm e}-7 x^{2}}{6 \ln \relax (2)}\)	\(23\)
risch	\(-20 x -\frac {7 x \,{\mathrm e}}{6 \ln \relax (2)}-\frac {7 x^{2}}{6 \ln \relax (2)}\)	\(23\)
norman	\(-\frac {7 x^{2}}{6 \ln \relax (2)}-\frac {\left (7 \,{\mathrm e}+120 \ln \relax (2)\right ) x}{6 \ln \relax (2)}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/6*(-120*ln(2)-7*exp(1)-14*x)/ln(2),x,method=_RETURNVERBOSE)

[Out]

-1/6*x*(7*x+7*exp(1)+120*ln(2))/ln(2)

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maxima [A]  time = 0.36, size = 22, normalized size = 1.22 \begin {gather*} -\frac {7 \, x^{2} + 7 \, x e + 120 \, x \log \relax (2)}{6 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(-120*log(2)-7*exp(1)-14*x)/log(2),x, algorithm="maxima")

[Out]

-1/6*(7*x^2 + 7*x*e + 120*x*log(2))/log(2)

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mupad [B]  time = 3.24, size = 20, normalized size = 1.11 \begin {gather*} -\frac {3\,{\left (\frac {7\,x}{3}+\frac {7\,\mathrm {e}}{6}+20\,\ln \relax (2)\right )}^2}{14\,\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((7*x)/3 + (7*exp(1))/6 + 20*log(2))/log(2),x)

[Out]

-(3*((7*x)/3 + (7*exp(1))/6 + 20*log(2))^2)/(14*log(2))

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sympy [A]  time = 0.05, size = 27, normalized size = 1.50 \begin {gather*} - \frac {7 x^{2}}{6 \log {\relax (2 )}} + \frac {x \left (- 120 \log {\relax (2 )} - 7 e\right )}{6 \log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/6*(-120*ln(2)-7*exp(1)-14*x)/ln(2),x)

[Out]

-7*x**2/(6*log(2)) + x*(-120*log(2) - 7*E)/(6*log(2))

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