Optimal. Leaf size=14 \[ \frac {25\ 2^{-72+8 x} x^2}{6561} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 9, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {12, 1607, 2227,
2207, 2225} \begin {gather*} \frac {25\ 2^{8 x-72} x^2}{6561} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 1607
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int 2^{-72+8 x} \left (50 x+200 x^2 \log (2)\right ) \, dx}{6561}\\ &=\frac {\int 2^{-72+8 x} x (50+200 x \log (2)) \, dx}{6561}\\ &=\frac {\int \left (25\ 2^{-71+8 x} x+25\ 2^{-69+8 x} x^2 \log (2)\right ) \, dx}{6561}\\ &=\frac {25 \int 2^{-71+8 x} x \, dx}{6561}+\frac {(25 \log (2)) \int 2^{-69+8 x} x^2 \, dx}{6561}\\ &=\frac {25\ 2^{-72+8 x} x^2}{6561}+\frac {25\ 2^{-74+8 x} x}{6561 \log (2)}-\frac {25 \int 2^{-69+8 x} x \, dx}{26244}-\frac {25 \int 2^{-71+8 x} \, dx}{52488 \log (2)}\\ &=\frac {25\ 2^{-72+8 x} x^2}{6561}-\frac {25\ 2^{-77+8 x}}{6561 \log ^2(2)}+\frac {25 \int 2^{-69+8 x} \, dx}{209952 \log (2)}\\ &=\frac {25\ 2^{-72+8 x} x^2}{6561}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 20, normalized size = 1.43 \begin {gather*} \frac {25\ 2^{-74+8 x} x^2 \log (16)}{6561 \log (2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs.
\(2(14)=28\).
time = 0.36, size = 76, normalized size = 5.43
method | result | size |
risch | \(\frac {25 \,2^{8 x} x^{2}}{30983446494107742247059456}\) | \(13\) |
gosper | \(\frac {25 \,{\mathrm e}^{8 \left (x -9\right ) \ln \left (2\right )} x^{2}}{6561}\) | \(15\) |
norman | \(\frac {25 \,{\mathrm e}^{8 \left (x -9\right ) \ln \left (2\right )} x^{2}}{6561}\) | \(15\) |
derivativedivides | \(\frac {\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \left (x \ln \left (2\right )-9 \ln \left (2\right )\right )}{1721302583005985680392192}+\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \ln \left (2\right )}{382511685112441262309376}+\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \left (x \ln \left (2\right )-9 \ln \left (2\right )\right )^{2}}{30983446494107742247059456 \ln \left (2\right )}}{\ln \left (2\right )}\) | \(76\) |
default | \(\frac {\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \left (x \ln \left (2\right )-9 \ln \left (2\right )\right )}{1721302583005985680392192}+\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \ln \left (2\right )}{382511685112441262309376}+\frac {25 \,{\mathrm e}^{8 x \ln \left (2\right )} \left (x \ln \left (2\right )-9 \ln \left (2\right )\right )^{2}}{30983446494107742247059456 \ln \left (2\right )}}{\ln \left (2\right )}\) | \(76\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (12) = 24\).
time = 0.46, size = 46, normalized size = 3.29 \begin {gather*} \frac {25 \, {\left (32 \, x^{2} \log \left (2\right )^{2} - 8 \, x \log \left (2\right ) + 1\right )} 2^{8 \, x}}{991470287811447751905902592 \, \log \left (2\right )^{2}} + \frac {25 \, {\left (8 \, x \log \left (2\right ) - 1\right )} 2^{8 \, x}}{991470287811447751905902592 \, \log \left (2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 12, normalized size = 0.86 \begin {gather*} \frac {25}{6561} \cdot 2^{8 \, x - 72} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 15, normalized size = 1.07 \begin {gather*} \frac {25 x^{2} e^{8 \left (x - 9\right ) \log {\left (2 \right )}}}{6561} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 16, normalized size = 1.14 \begin {gather*} \frac {25}{6561} \, x^{2} e^{\left (8 \, x \log \left (2\right ) - 72 \, \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.69, size = 10, normalized size = 0.71 \begin {gather*} \frac {25\,2^{8\,x}\,x^2}{30983446494107742247059456} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________