3.101.4 \(\int \frac {486 x+\log (2) (-238-\log (\frac {5}{2}))}{81 \log (2)} \, dx\)

Optimal. Leaf size=23 \[ x \left (-3+\frac {3 x}{\log (2)}+\frac {1}{81} \left (5-\log \left (\frac {5}{2}\right )\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {9} \begin {gather*} \frac {\left (486 x-\log (2) \left (238+\log \left (\frac {5}{2}\right )\right )\right )^2}{78732 \log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(486*x + Log[2]*(-238 - Log[5/2]))/(81*Log[2]),x]

[Out]

(486*x - Log[2]*(238 + Log[5/2]))^2/(78732*Log[2])

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 {\left (486 x-\log (2) \left (238+\log \left (\frac {5}{2}\right )\right )\right )^2}{78732 \log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} \frac {3 x^2}{\log (2)}+\frac {1}{81} x \left (-238-\log \left (\frac {5}{2}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(486*x + Log[2]*(-238 - Log[5/2]))/(81*Log[2]),x]

[Out]

(3*x^2)/Log[2] + (x*(-238 - Log[5/2]))/81

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fricas [A]  time = 1.21, size = 23, normalized size = 1.00 \begin {gather*} \frac {243 \, x^{2} + {\left (x \log \left (\frac {2}{5}\right ) - 238 \, x\right )} \log \relax (2)}{81 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/81*((log(2/5)-238)*log(2)+486*x)/log(2),x, algorithm="fricas")

[Out]

1/81*(243*x^2 + (x*log(2/5) - 238*x)*log(2))/log(2)

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giac [A]  time = 0.20, size = 20, normalized size = 0.87 \begin {gather*} \frac {x {\left (\log \left (\frac {2}{5}\right ) - 238\right )} \log \relax (2) + 243 \, x^{2}}{81 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/81*((log(2/5)-238)*log(2)+486*x)/log(2),x, algorithm="giac")

[Out]

1/81*(x*(log(2/5) - 238)*log(2) + 243*x^2)/log(2)

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maple [A]  time = 0.03, size = 21, normalized size = 0.91

method	result	size
gosper	\(\frac {x \left (\ln \relax (2) \ln \left (\frac {2}{5}\right )-238 \ln \relax (2)+243 x \right )}{81 \ln \relax (2)}\)	\(21\)
default	\(\frac {\left (\ln \left (\frac {2}{5}\right )-238\right ) \ln \relax (2) x +243 x^{2}}{81 \ln \relax (2)}\)	\(21\)
norman	\(\left (\frac {\ln \relax (2)}{81}-\frac {\ln \relax (5)}{81}-\frac {238}{81}\right ) x +\frac {3 x^{2}}{\ln \relax (2)}\)	\(23\)
risch	\(\frac {x \ln \relax (2)}{81}-\frac {x \ln \relax (5)}{81}-\frac {238 x}{81}+\frac {3 x^{2}}{\ln \relax (2)}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/81*((ln(2/5)-238)*ln(2)+486*x)/ln(2),x,method=_RETURNVERBOSE)

[Out]

1/81*x*(ln(2)*ln(2/5)-238*ln(2)+243*x)/ln(2)

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maxima [A]  time = 0.37, size = 20, normalized size = 0.87 \begin {gather*} \frac {x {\left (\log \left (\frac {2}{5}\right ) - 238\right )} \log \relax (2) + 243 \, x^{2}}{81 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/81*((log(2/5)-238)*log(2)+486*x)/log(2),x, algorithm="maxima")

[Out]

1/81*(x*(log(2/5) - 238)*log(2) + 243*x^2)/log(2)

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mupad [B]  time = 7.95, size = 20, normalized size = 0.87 \begin {gather*} \frac {{\left (6\,x+\frac {\ln \relax (2)\,\left (\ln \left (\frac {2}{5}\right )-238\right )}{81}\right )}^2}{12\,\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x + (log(2)*(log(2/5) - 238))/81)/log(2),x)

[Out]

(6*x + (log(2)*(log(2/5) - 238))/81)^2/(12*log(2))

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sympy [A]  time = 0.06, size = 22, normalized size = 0.96 \begin {gather*} \frac {3 x^{2}}{\log {\relax (2 )}} + x \left (- \frac {238}{81} - \frac {\log {\relax (5 )}}{81} + \frac {\log {\relax (2 )}}{81}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/81*((ln(2/5)-238)*ln(2)+486*x)/ln(2),x)

[Out]

3*x**2/log(2) + x*(-238/81 - log(5)/81 + log(2)/81)

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