3.64.81 \(\int \frac {1}{51} (125-50 x-25 \log (3)) \, dx\)

Optimal. Leaf size=10 \[ -\frac {25}{51} x (-5+x+\log (3)) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.50, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} -\frac {25}{204} (-2 x+5-\log (3))^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(125 - 50*x - 25*Log[3])/51,x]

[Out]

(-25*(5 - 2*x - Log[3])^2)/204

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 {25}{204} (5-2 x-\log (3))^2\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 15, normalized size = 1.50 \begin {gather*} -\frac {25}{51} \left (-5 x+x^2+x \log (3)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(125 - 50*x - 25*Log[3])/51,x]

[Out]

(-25*(-5*x + x^2 + x*Log[3]))/51

________________________________________________________________________________________

fricas [A]  time = 0.69, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25/51*log(3)-50/51*x+125/51,x, algorithm="fricas")

[Out]

-25/51*x^2 - 25/51*x*log(3) + 125/51*x

________________________________________________________________________________________

giac [A]  time = 0.24, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25/51*log(3)-50/51*x+125/51,x, algorithm="giac")

[Out]

-25/51*x^2 - 25/51*x*log(3) + 125/51*x

________________________________________________________________________________________

maple [A]  time = 0.06, size = 9, normalized size = 0.90

method	result	size
gosper	\(-\frac {25 x \left (\ln \relax (3)-5+x \right )}{51}\)	\(9\)
default	\(-\frac {25 x \ln \relax (3)}{51}-\frac {25 x^{2}}{51}+\frac {125 x}{51}\)	\(15\)
norman	\(\left (-\frac {25 \ln \relax (3)}{51}+\frac {125}{51}\right ) x -\frac {25 x^{2}}{51}\)	\(15\)
risch	\(-\frac {25 x \ln \relax (3)}{51}-\frac {25 x^{2}}{51}+\frac {125 x}{51}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-25/51*ln(3)-50/51*x+125/51,x,method=_RETURNVERBOSE)

[Out]

-25/51*x*(ln(3)-5+x)

________________________________________________________________________________________

maxima [A]  time = 0.41, size = 14, normalized size = 1.40 \begin {gather*} -\frac {25}{51} \, x^{2} - \frac {25}{51} \, x \log \relax (3) + \frac {125}{51} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25/51*log(3)-50/51*x+125/51,x, algorithm="maxima")

[Out]

-25/51*x^2 - 25/51*x*log(3) + 125/51*x

________________________________________________________________________________________

mupad [B]  time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} -\frac {25\,x\,\left (x+\ln \relax (3)-5\right )}{51} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(125/51 - (25*log(3))/51 - (50*x)/51,x)

[Out]

-(25*x*(x + log(3) - 5))/51

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 17, normalized size = 1.70 \begin {gather*} - \frac {25 x^{2}}{51} + x \left (\frac {125}{51} - \frac {25 \log {\relax (3 )}}{51}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25/51*ln(3)-50/51*x+125/51,x)

[Out]

-25*x**2/51 + x*(125/51 - 25*log(3)/51)

________________________________________________________________________________________