\(\int \frac {486 x+\log (2) (-238-\log (\frac {5}{2}))}{81 \log (2)} \, dx\) [10004]

Optimal result

Integrand size = 23, antiderivative size = 23 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=x \left (-3+\frac {3 x}{\log (2)}+\frac {1}{81} \left (5-\log \left (\frac {5}{2}\right )\right )\right ) \]

[Out]

(-238/81+1/81*ln(2/5)+3*x/ln(2))*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {9} \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {\left (486 x-\log (2) \left (238+\log \left (\frac {5}{2}\right )\right )\right )^2}{78732 \log (2)} \]

[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{align*} \text {integral}& = \frac {\left (486 x-\log (2) \left (238+\log \left (\frac {5}{2}\right )\right )\right )^2}{78732 \log (2)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {3 x^2}{\log (2)}+\frac {1}{81} x \left (-238-\log \left (\frac {5}{2}\right )\right ) \]

[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

Maple [A] (verified)

Time = 0.20 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91

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

[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)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {243 \, x^{2} + {\left (x \log \left (\frac {2}{5}\right ) - 238 \, x\right )} \log \left (2\right )}{81 \, \log \left (2\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {3 x^{2}}{\log {\left (2 \right )}} + x \left (- \frac {238}{81} - \frac {\log {\left (5 \right )}}{81} + \frac {\log {\left (2 \right )}}{81}\right ) \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {x {\left (\log \left (\frac {2}{5}\right ) - 238\right )} \log \left (2\right ) + 243 \, x^{2}}{81 \, \log \left (2\right )} \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {x {\left (\log \left (\frac {2}{5}\right ) - 238\right )} \log \left (2\right ) + 243 \, x^{2}}{81 \, \log \left (2\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 17.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {486 x+\log (2) \left (-238-\log \left (\frac {5}{2}\right )\right )}{81 \log (2)} \, dx=\frac {{\left (6\,x+\frac {\ln \left (2\right )\,\left (\ln \left (\frac {2}{5}\right )-238\right )}{81}\right )}^2}{12\,\ln \left (2\right )} \]

[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))