Optimal. Leaf size=474 \[ -\frac{2 b^{11/4} \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} \left (65 \sqrt{a} e+77 \sqrt{b} c\right ) \text{EllipticF}\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right ),\frac{1}{2}\right )}{5005 a^{7/4} \sqrt{a+b x^4}}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left (\sqrt{a}+\sqrt{b} x^2\right )}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}+\frac{4 b^{13/4} c \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{65 a^{7/4} \sqrt{a+b x^4}}+\frac{b^3 d \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}-\frac{b \sqrt{a+b x^4} \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right )}{240240}-\frac{\left (a+b x^4\right )^{3/2} \left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right )}{8580} \]
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Rubi [A] time = 0.549361, antiderivative size = 474, normalized size of antiderivative = 1., number of steps used = 16, number of rules used = 13, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.433, Rules used = {14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 835, 807, 266, 63, 208} \[ -\frac{2 b^{11/4} \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} \left (65 \sqrt{a} e+77 \sqrt{b} c\right ) F\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{5005 a^{7/4} \sqrt{a+b x^4}}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left (\sqrt{a}+\sqrt{b} x^2\right )}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}+\frac{4 b^{13/4} c \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{65 a^{7/4} \sqrt{a+b x^4}}+\frac{b^3 d \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}-\frac{b \sqrt{a+b x^4} \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right )}{240240}-\frac{\left (a+b x^4\right )^{3/2} \left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right )}{8580} \]
Antiderivative was successfully verified.
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Rule 14
Rule 1825
Rule 1833
Rule 1282
Rule 1198
Rule 220
Rule 1196
Rule 1252
Rule 835
Rule 807
Rule 266
Rule 63
Rule 208
Rubi steps
\begin{align*} \int \frac{\left (c+d x+e x^2+f x^3\right ) \left (a+b x^4\right )^{3/2}}{x^{14}} \, dx &=-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}-(6 b) \int \frac{\left (-\frac{c}{13}-\frac{d x}{12}-\frac{e x^2}{11}-\frac{f x^3}{10}\right ) \sqrt{a+b x^4}}{x^{10}} \, dx\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\left (12 b^2\right ) \int \frac{\frac{c}{117}+\frac{d x}{96}+\frac{e x^2}{77}+\frac{f x^3}{60}}{x^6 \sqrt{a+b x^4}} \, dx\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\left (12 b^2\right ) \int \left (\frac{\frac{c}{117}+\frac{e x^2}{77}}{x^6 \sqrt{a+b x^4}}+\frac{\frac{d}{96}+\frac{f x^2}{60}}{x^5 \sqrt{a+b x^4}}\right ) \, dx\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\left (12 b^2\right ) \int \frac{\frac{c}{117}+\frac{e x^2}{77}}{x^6 \sqrt{a+b x^4}} \, dx+\left (12 b^2\right ) \int \frac{\frac{d}{96}+\frac{f x^2}{60}}{x^5 \sqrt{a+b x^4}} \, dx\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\left (6 b^2\right ) \operatorname{Subst}\left (\int \frac{\frac{d}{96}+\frac{f x}{60}}{x^3 \sqrt{a+b x^2}} \, dx,x,x^2\right )-\frac{\left (12 b^2\right ) \int \frac{-\frac{5 a e}{77}+\frac{1}{39} b c x^2}{x^4 \sqrt{a+b x^4}} \, dx}{5 a}\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\frac{\left (4 b^2\right ) \int \frac{-\frac{1}{13} a b c-\frac{5}{77} a b e x^2}{x^2 \sqrt{a+b x^4}} \, dx}{5 a^2}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \frac{-\frac{a f}{30}+\frac{b d x}{96}}{x^2 \sqrt{a+b x^2}} \, dx,x,x^2\right )}{a}\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}-\frac{\left (4 b^2\right ) \int \frac{\frac{5}{77} a^2 b e+\frac{1}{13} a b^2 c x^2}{\sqrt{a+b x^4}} \, dx}{5 a^3}-\frac{\left (b^3 d\right ) \operatorname{Subst}\left (\int \frac{1}{x \sqrt{a+b x^2}} \, dx,x,x^2\right )}{32 a}\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\frac{\left (4 b^{7/2} c\right ) \int \frac{1-\frac{\sqrt{b} x^2}{\sqrt{a}}}{\sqrt{a+b x^4}} \, dx}{65 a^{3/2}}-\frac{\left (b^3 d\right ) \operatorname{Subst}\left (\int \frac{1}{x \sqrt{a+b x}} \, dx,x,x^4\right )}{64 a}-\frac{\left (4 b^3 \left (77 \sqrt{b} c+65 \sqrt{a} e\right )\right ) \int \frac{1}{\sqrt{a+b x^4}} \, dx}{5005 a^{3/2}}\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\frac{4 b^{13/4} c \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{65 a^{7/4} \sqrt{a+b x^4}}-\frac{2 b^{11/4} \left (77 \sqrt{b} c+65 \sqrt{a} e\right ) \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} F\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{5005 a^{7/4} \sqrt{a+b x^4}}-\frac{\left (b^2 d\right ) \operatorname{Subst}\left (\int \frac{1}{-\frac{a}{b}+\frac{x^2}{b}} \, dx,x,\sqrt{a+b x^4}\right )}{32 a}\\ &=-\frac{b \left (\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right ) \sqrt{a+b x^4}}{240240}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{\left (\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right ) \left (a+b x^4\right )^{3/2}}{8580}+\frac{b^3 d \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}+\frac{4 b^{13/4} c \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{65 a^{7/4} \sqrt{a+b x^4}}-\frac{2 b^{11/4} \left (77 \sqrt{b} c+65 \sqrt{a} e\right ) \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} F\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{5005 a^{7/4} \sqrt{a+b x^4}}\\ \end{align*}
Mathematica [C] time = 0.183965, size = 151, normalized size = 0.32 \[ -\frac{\sqrt{a+b x^4} \left (13 x^2 \left (11 x \left (a+b x^4\right )^2 \sqrt{\frac{b x^4}{a}+1} \left (a^3 f-b^3 d x^{10} \, _2F_1\left (\frac{5}{2},4;\frac{7}{2};\frac{b x^4}{a}+1\right )\right )+10 a^5 e \, _2F_1\left (-\frac{11}{4},-\frac{3}{2};-\frac{7}{4};-\frac{b x^4}{a}\right )\right )+110 a^5 c \, _2F_1\left (-\frac{13}{4},-\frac{3}{2};-\frac{9}{4};-\frac{b x^4}{a}\right )\right )}{1430 a^4 x^{13} \sqrt{\frac{b x^4}{a}+1}} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.02, size = 483, normalized size = 1. \begin{align*} -{\frac{ae}{11\,{x}^{11}}\sqrt{b{x}^{4}+a}}-{\frac{13\,be}{77\,{x}^{7}}\sqrt{b{x}^{4}+a}}-{\frac{4\,{b}^{2}e}{77\,a{x}^{3}}\sqrt{b{x}^{4}+a}}-{\frac{4\,e{b}^{3}}{77\,a}\sqrt{1-{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}\sqrt{1+{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}{\it EllipticF} \left ( x\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}},i \right ){\frac{1}{\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}}}}{\frac{1}{\sqrt{b{x}^{4}+a}}}}-{\frac{ac}{13\,{x}^{13}}\sqrt{b{x}^{4}+a}}-{\frac{5\,bc}{39\,{x}^{9}}\sqrt{b{x}^{4}+a}}-{\frac{4\,{b}^{2}c}{195\,a{x}^{5}}\sqrt{b{x}^{4}+a}}+{\frac{4\,{b}^{3}c}{65\,{a}^{2}x}\sqrt{b{x}^{4}+a}}-{{\frac{4\,i}{65}}c{b}^{{\frac{7}{2}}}\sqrt{1-{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}\sqrt{1+{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}{\it EllipticF} \left ( x\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}},i \right ){a}^{-{\frac{3}{2}}}{\frac{1}{\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}}}}{\frac{1}{\sqrt{b{x}^{4}+a}}}}+{{\frac{4\,i}{65}}c{b}^{{\frac{7}{2}}}\sqrt{1-{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}\sqrt{1+{i{x}^{2}\sqrt{b}{\frac{1}{\sqrt{a}}}}}{\it EllipticE} \left ( x\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}},i \right ){a}^{-{\frac{3}{2}}}{\frac{1}{\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}}}}{\frac{1}{\sqrt{b{x}^{4}+a}}}}-{\frac{7\,bd}{48\,{x}^{8}}\sqrt{b{x}^{4}+a}}-{\frac{{b}^{2}d}{32\,a{x}^{4}}\sqrt{b{x}^{4}+a}}+{\frac{{b}^{3}d}{32}\ln \left ({\frac{1}{{x}^{2}} \left ( 2\,a+2\,\sqrt{a}\sqrt{b{x}^{4}+a} \right ) } \right ){a}^{-{\frac{3}{2}}}}-{\frac{ad}{12\,{x}^{12}}\sqrt{b{x}^{4}+a}}-{\frac{f \left ({b}^{2}{x}^{8}+2\,ab{x}^{4}+{a}^{2} \right ) }{10\,{x}^{10}a}\sqrt{b{x}^{4}+a}} \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 (b x^{4} + a\right )}^{\frac{3}{2}}{\left (f x^{3} + e x^{2} + d x + c\right )}}{x^{14}}\,{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 f x^{7} + b e x^{6} + b d x^{5} + b c x^{4} + a f x^{3} + a e x^{2} + a d x + a c\right )} \sqrt{b x^{4} + a}}{x^{14}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 21.7902, size = 403, normalized size = 0.85 \begin{align*} \frac{a^{\frac{3}{2}} c \Gamma \left (- \frac{13}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{13}{4}, - \frac{1}{2} \\ - \frac{9}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 x^{13} \Gamma \left (- \frac{9}{4}\right )} + \frac{a^{\frac{3}{2}} e \Gamma \left (- \frac{11}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 x^{11} \Gamma \left (- \frac{7}{4}\right )} + \frac{\sqrt{a} b c \Gamma \left (- \frac{9}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 x^{9} \Gamma \left (- \frac{5}{4}\right )} + \frac{\sqrt{a} b e \Gamma \left (- \frac{7}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 x^{7} \Gamma \left (- \frac{3}{4}\right )} - \frac{a^{2} d}{12 \sqrt{b} x^{14} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{11 a \sqrt{b} d}{48 x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{17 b^{\frac{3}{2}} d}{96 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{5}{2}} d}{32 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} + \frac{b^{3} d \operatorname{asinh}{\left (\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right )}}{32 a^{\frac{3}{2}}} \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 (b x^{4} + a\right )}^{\frac{3}{2}}{\left (f x^{3} + e x^{2} + d x + c\right )}}{x^{14}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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