Optimal. Leaf size=26 \[ -6+\log \left (\frac {e^x}{2 \log \left (\left (x+\left (9+4 x^2\right )^2\right )^4\right )}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.38, antiderivative size = 21, normalized size of antiderivative = 0.81, number of steps
used = 4, number of rules used = 3, integrand size = 194, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6820, 6874,
6816} \begin {gather*} x-\log \left (\log \left (\left (16 x^4+72 x^2+x+81\right )^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4-576 x-256 x^3+\left (81+x+72 x^2+16 x^4\right ) \log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )}{\left (81+x+72 x^2+16 x^4\right ) \log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )} \, dx\\ &=\int \left (1-\frac {4 \left (1+144 x+64 x^3\right )}{\left (81+x+72 x^2+16 x^4\right ) \log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )}\right ) \, dx\\ &=x-4 \int \frac {1+144 x+64 x^3}{\left (81+x+72 x^2+16 x^4\right ) \log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )} \, dx\\ &=x-\log \left (\log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 21, normalized size = 0.81 \begin {gather*} x-\log \left (\log \left (\left (81+x+72 x^2+16 x^4\right )^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs.
\(2(23)=46\).
time = 0.30, size = 82, normalized size = 3.15
method | result | size |
default | \(x -\ln \left (\ln \left (65536 x^{16}+1179648 x^{14}+16384 x^{13}+9289728 x^{12}+221184 x^{11}+41805312 x^{10}+1244160 x^{9}+117586944 x^{8}+3732544 x^{7}+211678272 x^{6}+6298848 x^{5}+238155553 x^{4}+5669028 x^{3}+153094374 x^{2}+2125764 x +43046721\right )\right )\) | \(82\) |
norman | \(x -\ln \left (\ln \left (65536 x^{16}+1179648 x^{14}+16384 x^{13}+9289728 x^{12}+221184 x^{11}+41805312 x^{10}+1244160 x^{9}+117586944 x^{8}+3732544 x^{7}+211678272 x^{6}+6298848 x^{5}+238155553 x^{4}+5669028 x^{3}+153094374 x^{2}+2125764 x +43046721\right )\right )\) | \(82\) |
risch | \(x -\ln \left (\ln \left (65536 x^{16}+1179648 x^{14}+16384 x^{13}+9289728 x^{12}+221184 x^{11}+41805312 x^{10}+1244160 x^{9}+117586944 x^{8}+3732544 x^{7}+211678272 x^{6}+6298848 x^{5}+238155553 x^{4}+5669028 x^{3}+153094374 x^{2}+2125764 x +43046721\right )\right )\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 19, normalized size = 0.73 \begin {gather*} x - \log \left (\log \left (16 \, x^{4} + 72 \, x^{2} + x + 81\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 81 vs.
\(2 (23) = 46\).
time = 0.50, size = 81, normalized size = 3.12 \begin {gather*} x - \log \left (\log \left (65536 \, x^{16} + 1179648 \, x^{14} + 16384 \, x^{13} + 9289728 \, x^{12} + 221184 \, x^{11} + 41805312 \, x^{10} + 1244160 \, x^{9} + 117586944 \, x^{8} + 3732544 \, x^{7} + 211678272 \, x^{6} + 6298848 \, x^{5} + 238155553 \, x^{4} + 5669028 \, x^{3} + 153094374 \, x^{2} + 2125764 \, x + 43046721\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 80 vs.
\(2 (20) = 40\).
time = 0.14, size = 80, normalized size = 3.08 \begin {gather*} x - \log {\left (\log {\left (65536 x^{16} + 1179648 x^{14} + 16384 x^{13} + 9289728 x^{12} + 221184 x^{11} + 41805312 x^{10} + 1244160 x^{9} + 117586944 x^{8} + 3732544 x^{7} + 211678272 x^{6} + 6298848 x^{5} + 238155553 x^{4} + 5669028 x^{3} + 153094374 x^{2} + 2125764 x + 43046721 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 81 vs.
\(2 (23) = 46\).
time = 0.47, size = 81, normalized size = 3.12 \begin {gather*} x - \log \left (\log \left (65536 \, x^{16} + 1179648 \, x^{14} + 16384 \, x^{13} + 9289728 \, x^{12} + 221184 \, x^{11} + 41805312 \, x^{10} + 1244160 \, x^{9} + 117586944 \, x^{8} + 3732544 \, x^{7} + 211678272 \, x^{6} + 6298848 \, x^{5} + 238155553 \, x^{4} + 5669028 \, x^{3} + 153094374 \, x^{2} + 2125764 \, x + 43046721\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.01, size = 81, normalized size = 3.12 \begin {gather*} x-\ln \left (\ln \left (65536\,x^{16}+1179648\,x^{14}+16384\,x^{13}+9289728\,x^{12}+221184\,x^{11}+41805312\,x^{10}+1244160\,x^9+117586944\,x^8+3732544\,x^7+211678272\,x^6+6298848\,x^5+238155553\,x^4+5669028\,x^3+153094374\,x^2+2125764\,x+43046721\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________