Optimal. Leaf size=764 \[ -\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \left (7 a^{2/3} \sqrt [3]{b} e-5 \left (1-\sqrt{3}\right ) (b c-4 a f)\right ) \text{EllipticF}\left (\sin ^{-1}\left (\frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}\right ),-7-4 \sqrt{3}\right )}{2240 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}-\frac{27 b^{7/3} \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 \left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )}+\frac{27 b^2 \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 x}+\frac{27 \sqrt [4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} (b c-4 a f) E\left (\sin ^{-1}\left (\frac{\sqrt [3]{b} x+\left (1-\sqrt{3}\right ) \sqrt [3]{a}}{\sqrt [3]{b} x+\left (1+\sqrt{3}\right ) \sqrt [3]{a}}\right )|-7-4 \sqrt{3}\right )}{896 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}+\frac{b^2 (b d-6 a g) \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{24 a^{3/2}}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}-\frac{b \sqrt{a+b x^3} \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right )}{1680}-\frac{\left (a+b x^3\right )^{3/2} \left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right )}{2520} \]
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Rubi [A] time = 1.33014, antiderivative size = 764, normalized size of antiderivative = 1., number of steps used = 13, number of rules used = 10, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877} \[ -\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \left (7 a^{2/3} \sqrt [3]{b} e-5 \left (1-\sqrt{3}\right ) (b c-4 a f)\right ) F\left (\sin ^{-1}\left (\frac{\sqrt [3]{b} x+\left (1-\sqrt{3}\right ) \sqrt [3]{a}}{\sqrt [3]{b} x+\left (1+\sqrt{3}\right ) \sqrt [3]{a}}\right )|-7-4 \sqrt{3}\right )}{2240 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}-\frac{27 b^{7/3} \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 \left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )}+\frac{27 b^2 \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 x}+\frac{27 \sqrt [4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} (b c-4 a f) E\left (\sin ^{-1}\left (\frac{\sqrt [3]{b} x+\left (1-\sqrt{3}\right ) \sqrt [3]{a}}{\sqrt [3]{b} x+\left (1+\sqrt{3}\right ) \sqrt [3]{a}}\right )|-7-4 \sqrt{3}\right )}{896 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}+\frac{b^2 (b d-6 a g) \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{24 a^{3/2}}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}-\frac{b \sqrt{a+b x^3} \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right )}{1680}-\frac{\left (a+b x^3\right )^{3/2} \left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right )}{2520} \]
Antiderivative was successfully verified.
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Rule 14
Rule 1825
Rule 1835
Rule 1832
Rule 266
Rule 63
Rule 208
Rule 1878
Rule 218
Rule 1877
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^{3/2} \left (c+d x+e x^2+f x^3+g x^4\right )}{x^{11}} \, dx &=-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}-\frac{1}{2} (9 b) \int \frac{\sqrt{a+b x^3} \left (-\frac{c}{10}-\frac{d x}{9}-\frac{e x^2}{8}-\frac{f x^3}{7}-\frac{g x^4}{6}\right )}{x^8} \, dx\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{1}{4} \left (27 b^2\right ) \int \frac{\frac{c}{70}+\frac{d x}{54}+\frac{e x^2}{40}+\frac{f x^3}{28}+\frac{g x^4}{18}}{x^5 \sqrt{a+b x^3}} \, dx\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}-\frac{\left (27 b^2\right ) \int \frac{-\frac{4 a d}{27}-\frac{a e x}{5}+\frac{1}{14} (b c-4 a f) x^2-\frac{4}{9} a g x^3}{x^4 \sqrt{a+b x^3}} \, dx}{32 a}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{\left (9 b^2\right ) \int \frac{\frac{6 a^2 e}{5}-\frac{3}{7} a (b c-4 a f) x-\frac{4}{9} a (b d-6 a g) x^2}{x^3 \sqrt{a+b x^3}} \, dx}{64 a^2}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}-\frac{\left (9 b^2\right ) \int \frac{\frac{12}{7} a^2 (b c-4 a f)+\frac{16}{9} a^2 (b d-6 a g) x+\frac{6}{5} a^2 b e x^2}{x^2 \sqrt{a+b x^3}} \, dx}{256 a^3}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^2 (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 x}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{\left (9 b^2\right ) \int \frac{-\frac{32}{9} a^3 (b d-6 a g)-\frac{12}{5} a^3 b e x-\frac{12}{7} a^2 b (b c-4 a f) x^2}{x \sqrt{a+b x^3}} \, dx}{512 a^4}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^2 (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 x}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{\left (9 b^2\right ) \int \frac{-\frac{12}{5} a^3 b e-\frac{12}{7} a^2 b (b c-4 a f) x}{\sqrt{a+b x^3}} \, dx}{512 a^4}-\frac{\left (b^2 (b d-6 a g)\right ) \int \frac{1}{x \sqrt{a+b x^3}} \, dx}{16 a}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^2 (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 x}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}-\frac{\left (27 b^{8/3} (b c-4 a f)\right ) \int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\sqrt{a+b x^3}} \, dx}{896 a^2}-\frac{\left (27 b^{8/3} \left (7 a^{2/3} \sqrt [3]{b} e-5 \left (1-\sqrt{3}\right ) (b c-4 a f)\right )\right ) \int \frac{1}{\sqrt{a+b x^3}} \, dx}{4480 a^{5/3}}-\frac{\left (b^2 (b d-6 a g)\right ) \operatorname{Subst}\left (\int \frac{1}{x \sqrt{a+b x}} \, dx,x,x^3\right )}{48 a}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^2 (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 x}-\frac{27 b^{7/3} (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 \left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{27 \sqrt [4]{3} \sqrt{2-\sqrt{3}} b^{7/3} (b c-4 a f) \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} E\left (\sin ^{-1}\left (\frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}\right )|-7-4 \sqrt{3}\right )}{896 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left (7 a^{2/3} \sqrt [3]{b} e-5 \left (1-\sqrt{3}\right ) (b c-4 a f)\right ) \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} F\left (\sin ^{-1}\left (\frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}\right )|-7-4 \sqrt{3}\right )}{2240 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}-\frac{(b (b d-6 a g)) \operatorname{Subst}\left (\int \frac{1}{-\frac{a}{b}+\frac{x^2}{b}} \, dx,x,\sqrt{a+b x^3}\right )}{24 a}\\ &=-\frac{b \left (\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right ) \sqrt{a+b x^3}}{1680}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^2 (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 x}-\frac{27 b^{7/3} (b c-4 a f) \sqrt{a+b x^3}}{448 a^2 \left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )}-\frac{\left (\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right ) \left (a+b x^3\right )^{3/2}}{2520}+\frac{b^2 (b d-6 a g) \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{24 a^{3/2}}+\frac{27 \sqrt [4]{3} \sqrt{2-\sqrt{3}} b^{7/3} (b c-4 a f) \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} E\left (\sin ^{-1}\left (\frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}\right )|-7-4 \sqrt{3}\right )}{896 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left (7 a^{2/3} \sqrt [3]{b} e-5 \left (1-\sqrt{3}\right ) (b c-4 a f)\right ) \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{\frac{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} F\left (\sin ^{-1}\left (\frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}\right )|-7-4 \sqrt{3}\right )}{2240 a^{5/3} \sqrt{\frac{\sqrt [3]{a} \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right )^2}} \sqrt{a+b x^3}}\\ \end{align*}
Mathematica [C] time = 0.506918, size = 227, normalized size = 0.3 \[ -\frac{\sqrt{a+b x^3} \left (2 x^3 \left (35 a^3 g x \left (3 b^2 x^6 \tanh ^{-1}\left (\sqrt{\frac{b x^3}{a}+1}\right )+a \left (2 a+5 b x^3\right ) \sqrt{\frac{b x^3}{a}+1}\right )+60 a^5 f \, _2F_1\left (-\frac{7}{3},-\frac{3}{2};-\frac{4}{3};-\frac{b x^3}{a}\right )-56 b^3 d x^7 \left (a+b x^3\right )^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left (\frac{5}{2},4;\frac{7}{2};\frac{b x^3}{a}+1\right )\right )+84 a^5 c \, _2F_1\left (-\frac{10}{3},-\frac{3}{2};-\frac{7}{3};-\frac{b x^3}{a}\right )+105 a^5 e x^2 \, _2F_1\left (-\frac{8}{3},-\frac{3}{2};-\frac{5}{3};-\frac{b x^3}{a}\right )\right )}{840 a^4 x^{10} \sqrt{\frac{b x^3}{a}+1}} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.008, size = 1470, normalized size = 1.9 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (g x^{4} + f x^{3} + e x^{2} + d x + c\right )}{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{x^{11}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (b g x^{7} + b f x^{6} + b e x^{5} +{\left (b d + a g\right )} x^{4} + a e x^{2} +{\left (b c + a f\right )} x^{3} + a d x + a c\right )} \sqrt{b x^{3} + a}}{x^{11}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 24.3077, size = 576, normalized size = 0.75 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (g x^{4} + f x^{3} + e x^{2} + d x + c\right )}{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{x^{11}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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