Optimal. Leaf size=479 \[ -\frac {15 b^2 d^4 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{4 e^6}+\frac {20 b^2 d^3 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{9 e^6}-\frac {15 b^2 d^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{16 e^6}+\frac {6 b^2 d n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{25 e^6}-\frac {b^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{36 e^6}+\frac {6 b^2 d^5 n^2}{e^5 \sqrt [3]{x}}-\frac {b^2 d^6 n^2 \log ^2\left (d+\frac {e}{\sqrt [3]{x}}\right )}{2 e^6}-\frac {6 b d^5 n \left (d+\frac {e}{\sqrt [3]{x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{e^6}+\frac {15 b d^4 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{2 e^6}-\frac {20 b d^3 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{3 e^6}+\frac {15 b d^2 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^4 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{4 e^6}-\frac {6 b d n \left (d+\frac {e}{\sqrt [3]{x}}\right )^5 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{5 e^6}+\frac {b n \left (d+\frac {e}{\sqrt [3]{x}}\right )^6 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{6 e^6}+\frac {b d^6 n \log \left (d+\frac {e}{\sqrt [3]{x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{e^6}-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.32, antiderivative size = 479, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 8, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2504, 2445,
2458, 45, 2372, 12, 14, 2338} \begin {gather*} \frac {b d^6 n \log \left (d+\frac {e}{\sqrt [3]{x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{e^6}-\frac {6 b d^5 n \left (d+\frac {e}{\sqrt [3]{x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{e^6}+\frac {15 b d^4 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{2 e^6}-\frac {20 b d^3 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{3 e^6}+\frac {15 b d^2 n \left (d+\frac {e}{\sqrt [3]{x}}\right )^4 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{4 e^6}-\frac {6 b d n \left (d+\frac {e}{\sqrt [3]{x}}\right )^5 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{5 e^6}+\frac {b n \left (d+\frac {e}{\sqrt [3]{x}}\right )^6 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )}{6 e^6}-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}-\frac {b^2 d^6 n^2 \log ^2\left (d+\frac {e}{\sqrt [3]{x}}\right )}{2 e^6}+\frac {6 b^2 d^5 n^2}{e^5 \sqrt [3]{x}}-\frac {15 b^2 d^4 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{4 e^6}+\frac {20 b^2 d^3 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{9 e^6}-\frac {15 b^2 d^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{16 e^6}+\frac {6 b^2 d n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{25 e^6}-\frac {b^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{36 e^6} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 45
Rule 2338
Rule 2372
Rule 2445
Rule 2458
Rule 2504
Rubi steps
\begin {align*} \int \frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{x^3} \, dx &=-\left (3 \text {Subst}\left (\int x^5 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx,x,\frac {1}{\sqrt [3]{x}}\right )\right )\\ &=-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}+(b e n) \text {Subst}\left (\int \frac {x^6 \left (a+b \log \left (c (d+e x)^n\right )\right )}{d+e x} \, dx,x,\frac {1}{\sqrt [3]{x}}\right )\\ &=-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}+(b n) \text {Subst}\left (\int \frac {\left (-\frac {d}{e}+\frac {x}{e}\right )^6 \left (a+b \log \left (c x^n\right )\right )}{x} \, dx,x,d+\frac {e}{\sqrt [3]{x}}\right )\\ &=-\frac {1}{60} b n \left (\frac {360 d^5 \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}-\frac {450 d^4 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{e^6}+\frac {400 d^3 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{e^6}-\frac {225 d^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{e^6}+\frac {72 d \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{e^6}-\frac {10 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{e^6}-\frac {60 d^6 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}-\left (b^2 n^2\right ) \text {Subst}\left (\int \frac {x \left (-360 d^5+450 d^4 x-400 d^3 x^2+225 d^2 x^3-72 d x^4+10 x^5\right )+60 d^6 \log (x)}{60 e^6 x} \, dx,x,d+\frac {e}{\sqrt [3]{x}}\right )\\ &=-\frac {1}{60} b n \left (\frac {360 d^5 \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}-\frac {450 d^4 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{e^6}+\frac {400 d^3 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{e^6}-\frac {225 d^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{e^6}+\frac {72 d \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{e^6}-\frac {10 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{e^6}-\frac {60 d^6 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}-\frac {\left (b^2 n^2\right ) \text {Subst}\left (\int \frac {x \left (-360 d^5+450 d^4 x-400 d^3 x^2+225 d^2 x^3-72 d x^4+10 x^5\right )+60 d^6 \log (x)}{x} \, dx,x,d+\frac {e}{\sqrt [3]{x}}\right )}{60 e^6}\\ &=-\frac {1}{60} b n \left (\frac {360 d^5 \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}-\frac {450 d^4 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{e^6}+\frac {400 d^3 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{e^6}-\frac {225 d^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{e^6}+\frac {72 d \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{e^6}-\frac {10 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{e^6}-\frac {60 d^6 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}-\frac {\left (b^2 n^2\right ) \text {Subst}\left (\int \left (-360 d^5+450 d^4 x-400 d^3 x^2+225 d^2 x^3-72 d x^4+10 x^5+\frac {60 d^6 \log (x)}{x}\right ) \, dx,x,d+\frac {e}{\sqrt [3]{x}}\right )}{60 e^6}\\ &=-\frac {15 b^2 d^4 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{4 e^6}+\frac {20 b^2 d^3 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{9 e^6}-\frac {15 b^2 d^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{16 e^6}+\frac {6 b^2 d n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{25 e^6}-\frac {b^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{36 e^6}+\frac {6 b^2 d^5 n^2}{e^5 \sqrt [3]{x}}-\frac {1}{60} b n \left (\frac {360 d^5 \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}-\frac {450 d^4 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{e^6}+\frac {400 d^3 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{e^6}-\frac {225 d^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{e^6}+\frac {72 d \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{e^6}-\frac {10 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{e^6}-\frac {60 d^6 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}-\frac {\left (b^2 d^6 n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\\ &=-\frac {15 b^2 d^4 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{4 e^6}+\frac {20 b^2 d^3 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{9 e^6}-\frac {15 b^2 d^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{16 e^6}+\frac {6 b^2 d n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{25 e^6}-\frac {b^2 n^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{36 e^6}+\frac {6 b^2 d^5 n^2}{e^5 \sqrt [3]{x}}-\frac {b^2 d^6 n^2 \log ^2\left (d+\frac {e}{\sqrt [3]{x}}\right )}{2 e^6}-\frac {1}{60} b n \left (\frac {360 d^5 \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}-\frac {450 d^4 \left (d+\frac {e}{\sqrt [3]{x}}\right )^2}{e^6}+\frac {400 d^3 \left (d+\frac {e}{\sqrt [3]{x}}\right )^3}{e^6}-\frac {225 d^2 \left (d+\frac {e}{\sqrt [3]{x}}\right )^4}{e^6}+\frac {72 d \left (d+\frac {e}{\sqrt [3]{x}}\right )^5}{e^6}-\frac {10 \left (d+\frac {e}{\sqrt [3]{x}}\right )^6}{e^6}-\frac {60 d^6 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )}{e^6}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )-\frac {\left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )\right )^2}{2 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.24, size = 698, normalized size = 1.46 \begin {gather*} \frac {-1800 a^2 e^6+600 a b e^6 n-100 b^2 e^6 n^2-720 a b d e^5 n \sqrt [3]{x}+264 b^2 d e^5 n^2 \sqrt [3]{x}+900 a b d^2 e^4 n x^{2/3}-555 b^2 d^2 e^4 n^2 x^{2/3}-1200 a b d^3 e^3 n x+1140 b^2 d^3 e^3 n^2 x+1800 a b d^4 e^2 n x^{4/3}-2610 b^2 d^4 e^2 n^2 x^{4/3}-3600 a b d^5 e n x^{5/3}+8820 b^2 d^5 e n^2 x^{5/3}-5220 b^2 d^6 n^2 x^2 \log \left (d+\frac {e}{\sqrt [3]{x}}\right )-3600 a b e^6 \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )+600 b^2 e^6 n \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )-720 b^2 d e^5 n \sqrt [3]{x} \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )+900 b^2 d^2 e^4 n x^{2/3} \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )-1200 b^2 d^3 e^3 n x \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )+1800 b^2 d^4 e^2 n x^{4/3} \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )-3600 b^2 d^5 e n x^{5/3} \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )-3600 b^2 d^6 n x^2 \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )-1800 b^2 e^6 \log ^2\left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right )+3600 a b d^6 n x^2 \log \left (e+d \sqrt [3]{x}\right )+3600 b^2 d^6 n x^2 \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right ) \log \left (e+d \sqrt [3]{x}\right )-1800 b^2 d^6 n^2 x^2 \log ^2\left (e+d \sqrt [3]{x}\right )+3600 a b d^6 n x^2 \log \left (-\frac {e}{d \sqrt [3]{x}}\right )+3600 b^2 d^6 n x^2 \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^n\right ) \log \left (-\frac {e}{d \sqrt [3]{x}}\right )+3600 b^2 d^6 n^2 x^2 \log \left (e+d \sqrt [3]{x}\right ) \log \left (-\frac {d \sqrt [3]{x}}{e}\right )+3600 b^2 d^6 n^2 x^2 \text {Li}_2\left (1+\frac {e}{d \sqrt [3]{x}}\right )+3600 b^2 d^6 n^2 x^2 \text {Li}_2\left (1+\frac {d \sqrt [3]{x}}{e}\right )}{3600 e^6 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \ln \left (c \left (d +\frac {e}{x^{\frac {1}{3}}}\right )^{n}\right )\right )^{2}}{x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 379, normalized size = 0.79 \begin {gather*} \frac {1}{60} \, {\left (60 \, d^{6} e^{\left (-7\right )} \log \left (d x^{\frac {1}{3}} + e\right ) - 20 \, d^{6} e^{\left (-7\right )} \log \left (x\right ) - \frac {{\left (60 \, d^{5} x^{\frac {5}{3}} - 30 \, d^{4} x^{\frac {4}{3}} e + 20 \, d^{3} x e^{2} - 15 \, d^{2} x^{\frac {2}{3}} e^{3} + 12 \, d x^{\frac {1}{3}} e^{4} - 10 \, e^{5}\right )} e^{\left (-6\right )}}{x^{2}}\right )} a b n e + \frac {1}{3600} \, {\left (60 \, {\left (60 \, d^{6} e^{\left (-7\right )} \log \left (d x^{\frac {1}{3}} + e\right ) - 20 \, d^{6} e^{\left (-7\right )} \log \left (x\right ) - \frac {{\left (60 \, d^{5} x^{\frac {5}{3}} - 30 \, d^{4} x^{\frac {4}{3}} e + 20 \, d^{3} x e^{2} - 15 \, d^{2} x^{\frac {2}{3}} e^{3} + 12 \, d x^{\frac {1}{3}} e^{4} - 10 \, e^{5}\right )} e^{\left (-6\right )}}{x^{2}}\right )} n e \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{n}\right ) - \frac {{\left (1800 \, d^{6} x^{2} \log \left (d x^{\frac {1}{3}} + e\right )^{2} + 200 \, d^{6} x^{2} \log \left (x\right )^{2} - 2940 \, d^{6} x^{2} \log \left (x\right ) - 8820 \, d^{5} x^{\frac {5}{3}} e + 2610 \, d^{4} x^{\frac {4}{3}} e^{2} - 1140 \, d^{3} x e^{3} + 555 \, d^{2} x^{\frac {2}{3}} e^{4} - 264 \, d x^{\frac {1}{3}} e^{5} - 60 \, {\left (20 \, d^{6} x^{2} \log \left (x\right ) - 147 \, d^{6} x^{2}\right )} \log \left (d x^{\frac {1}{3}} + e\right ) + 100 \, e^{6}\right )} n^{2} e^{\left (-6\right )}}{x^{2}}\right )} b^{2} - \frac {b^{2} \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{n}\right )^{2}}{2 \, x^{2}} - \frac {a b \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{n}\right )}{x^{2}} - \frac {a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.50, size = 550, normalized size = 1.15 \begin {gather*} \frac {{\left (1800 \, {\left (b^{2} x^{2} - b^{2}\right )} e^{6} \log \left (c\right )^{2} + 1800 \, {\left (b^{2} d^{6} n^{2} x^{2} - b^{2} n^{2} e^{6}\right )} \log \left (\frac {d x + x^{\frac {2}{3}} e}{x}\right )^{2} - 100 \, {\left (b^{2} n^{2} - 6 \, a b n - {\left (b^{2} n^{2} - 6 \, a b n + 18 \, a^{2}\right )} x^{2} + 18 \, a^{2}\right )} e^{6} - 60 \, {\left ({\left (19 \, b^{2} d^{3} n^{2} - 20 \, a b d^{3} n\right )} x^{2} - {\left (19 \, b^{2} d^{3} n^{2} - 20 \, a b d^{3} n\right )} x\right )} e^{3} + 600 \, {\left ({\left (b^{2} n - {\left (b^{2} n - 6 \, a b\right )} x^{2} - 6 \, a b\right )} e^{6} + 2 \, {\left (b^{2} d^{3} n x^{2} - b^{2} d^{3} n x\right )} e^{3}\right )} \log \left (c\right ) - 60 \, {\left (20 \, b^{2} d^{3} n^{2} x e^{3} + 3 \, {\left (49 \, b^{2} d^{6} n^{2} - 20 \, a b d^{6} n\right )} x^{2} - 10 \, {\left (b^{2} n^{2} - 6 \, a b n\right )} e^{6} - 60 \, {\left (b^{2} d^{6} n x^{2} - b^{2} n e^{6}\right )} \log \left (c\right ) + 15 \, {\left (4 \, b^{2} d^{5} n^{2} x e - b^{2} d^{2} n^{2} e^{4}\right )} x^{\frac {2}{3}} - 6 \, {\left (5 \, b^{2} d^{4} n^{2} x e^{2} - 2 \, b^{2} d n^{2} e^{5}\right )} x^{\frac {1}{3}}\right )} \log \left (\frac {d x + x^{\frac {2}{3}} e}{x}\right ) + 15 \, {\left (12 \, {\left (49 \, b^{2} d^{5} n^{2} - 20 \, a b d^{5} n\right )} x e - {\left (37 \, b^{2} d^{2} n^{2} - 60 \, a b d^{2} n\right )} e^{4} - 60 \, {\left (4 \, b^{2} d^{5} n x e - b^{2} d^{2} n e^{4}\right )} \log \left (c\right )\right )} x^{\frac {2}{3}} - 6 \, {\left (15 \, {\left (29 \, b^{2} d^{4} n^{2} - 20 \, a b d^{4} n\right )} x e^{2} - 4 \, {\left (11 \, b^{2} d n^{2} - 30 \, a b d n\right )} e^{5} - 60 \, {\left (5 \, b^{2} d^{4} n x e^{2} - 2 \, b^{2} d n e^{5}\right )} \log \left (c\right )\right )} x^{\frac {1}{3}}\right )} e^{\left (-6\right )}}{3600 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \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. 1639 vs.
\(2 (418) = 836\).
time = 5.46, size = 1639, normalized size = 3.42 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.76, size = 439, normalized size = 0.92 \begin {gather*} \frac {b^2\,d^6\,{\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}^2}{2\,e^6}-\frac {b^2\,{\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}^2}{2\,x^2}-\frac {b^2\,n^2}{36\,x^2}-\frac {a\,b\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{x^2}-\frac {a^2}{2\,x^2}+\frac {a\,b\,n}{6\,x^2}+\frac {b^2\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{6\,x^2}-\frac {49\,b^2\,d^6\,n^2\,\ln \left (d+\frac {e}{x^{1/3}}\right )}{20\,e^6}+\frac {19\,b^2\,d^3\,n^2}{60\,e^3\,x}-\frac {37\,b^2\,d^2\,n^2}{240\,e^2\,x^{4/3}}-\frac {29\,b^2\,d^4\,n^2}{40\,e^4\,x^{2/3}}+\frac {49\,b^2\,d^5\,n^2}{20\,e^5\,x^{1/3}}+\frac {11\,b^2\,d\,n^2}{150\,e\,x^{5/3}}-\frac {b^2\,d^3\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{3\,e^3\,x}+\frac {b^2\,d^2\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{4\,e^2\,x^{4/3}}+\frac {b^2\,d^4\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{2\,e^4\,x^{2/3}}-\frac {b^2\,d^5\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{e^5\,x^{1/3}}-\frac {a\,b\,d\,n}{5\,e\,x^{5/3}}+\frac {a\,b\,d^6\,n\,\ln \left (d+\frac {e}{x^{1/3}}\right )}{e^6}-\frac {b^2\,d\,n\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^n\right )}{5\,e\,x^{5/3}}-\frac {a\,b\,d^3\,n}{3\,e^3\,x}+\frac {a\,b\,d^2\,n}{4\,e^2\,x^{4/3}}+\frac {a\,b\,d^4\,n}{2\,e^4\,x^{2/3}}-\frac {a\,b\,d^5\,n}{e^5\,x^{1/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________