Optimal. Leaf size=449 \[ -\frac{2 b^{9/4} \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} \left (15 \sqrt{b} d-77 \sqrt{a} f\right ) \text{EllipticF}\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right ),\frac{1}{2}\right )}{1155 a^{5/4} \sqrt{a+b x^4}}+\frac{b^3 c \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}-\frac{4 b^{9/4} f \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{b \sqrt{a+b x^4} \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right )}{18480}-\frac{\left (a+b x^4\right )^{3/2} \left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right )}{1980} \]
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Rubi [A] time = 0.490132, antiderivative size = 449, normalized size of antiderivative = 1., number of steps used = 15, number of rules used = 13, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.433, Rules used = {14, 1825, 1833, 1252, 835, 807, 266, 63, 208, 1282, 1198, 220, 1196} \[ \frac{b^3 c \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}-\frac{2 b^{9/4} \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} \left (15 \sqrt{b} d-77 \sqrt{a} f\right ) F\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} f \left (\sqrt{a}+\sqrt{b} x^2\right ) \sqrt{\frac{a+b x^4}{\left (\sqrt{a}+\sqrt{b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac{\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac{1}{2}\right )}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{b \sqrt{a+b x^4} \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right )}{18480}-\frac{\left (a+b x^4\right )^{3/2} \left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right )}{1980} \]
Antiderivative was successfully verified.
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Rule 14
Rule 1825
Rule 1833
Rule 1252
Rule 835
Rule 807
Rule 266
Rule 63
Rule 208
Rule 1282
Rule 1198
Rule 220
Rule 1196
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^{13}} \, dx &=-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}-(6 b) \int \frac{\left (-\frac{c}{12}-\frac{d x}{11}-\frac{e x^2}{10}-\frac{f x^3}{9}\right ) \sqrt{a+b x^4}}{x^9} \, dx\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\left (12 b^2\right ) \int \frac{\frac{c}{96}+\frac{d x}{77}+\frac{e x^2}{60}+\frac{f x^3}{45}}{x^5 \sqrt{a+b x^4}} \, dx\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\left (12 b^2\right ) \int \left (\frac{\frac{c}{96}+\frac{e x^2}{60}}{x^5 \sqrt{a+b x^4}}+\frac{\frac{d}{77}+\frac{f x^2}{45}}{x^4 \sqrt{a+b x^4}}\right ) \, dx\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\left (12 b^2\right ) \int \frac{\frac{c}{96}+\frac{e x^2}{60}}{x^5 \sqrt{a+b x^4}} \, dx+\left (12 b^2\right ) \int \frac{\frac{d}{77}+\frac{f x^2}{45}}{x^4 \sqrt{a+b x^4}} \, dx\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\left (6 b^2\right ) \operatorname{Subst}\left (\int \frac{\frac{c}{96}+\frac{e x}{60}}{x^3 \sqrt{a+b x^2}} \, dx,x,x^2\right )-\frac{\left (4 b^2\right ) \int \frac{-\frac{a f}{15}+\frac{1}{77} b d x^2}{x^2 \sqrt{a+b x^4}} \, dx}{a}\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\frac{\left (4 b^2\right ) \int \frac{-\frac{1}{77} a b d+\frac{1}{15} a b f x^2}{\sqrt{a+b x^4}} \, dx}{a^2}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \frac{-\frac{a e}{30}+\frac{b c x}{96}}{x^2 \sqrt{a+b x^2}} \, dx,x,x^2\right )}{a}\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}-\frac{\left (b^3 c\right ) \operatorname{Subst}\left (\int \frac{1}{x \sqrt{a+b x^2}} \, dx,x,x^2\right )}{32 a}-\frac{\left (4 b^{5/2} f\right ) \int \frac{1-\frac{\sqrt{b} x^2}{\sqrt{a}}}{\sqrt{a+b x^4}} \, dx}{15 \sqrt{a}}-\frac{\left (4 b^{5/2} \left (15 \sqrt{b} d-77 \sqrt{a} f\right )\right ) \int \frac{1}{\sqrt{a+b x^4}} \, dx}{1155 a}\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}-\frac{4 b^{9/4} f \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 )}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{9/4} \left (15 \sqrt{b} d-77 \sqrt{a} f\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 )}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{\left (b^3 c\right ) \operatorname{Subst}\left (\int \frac{1}{x \sqrt{a+b x}} \, dx,x,x^4\right )}{64 a}\\ &=-\frac{b \left (\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}-\frac{4 b^{9/4} f \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 )}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{9/4} \left (15 \sqrt{b} d-77 \sqrt{a} f\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 )}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{\left (b^2 c\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{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right ) \sqrt{a+b x^4}}{18480}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left (\sqrt{a}+\sqrt{b} x^2\right )}-\frac{\left (\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right ) \left (a+b x^4\right )^{3/2}}{1980}+\frac{b^3 c \tanh ^{-1}\left (\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right )}{32 a^{3/2}}-\frac{4 b^{9/4} f \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 )}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{9/4} \left (15 \sqrt{b} d-77 \sqrt{a} f\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 )}{1155 a^{5/4} \sqrt{a+b x^4}}\\ \end{align*}
Mathematica [C] time = 0.191164, size = 149, normalized size = 0.33 \[ -\frac{\sqrt{a+b x^4} \left (11 x \left (9 \left (a+b x^4\right )^2 \sqrt{\frac{b x^4}{a}+1} \left (a^3 e-b^3 c x^{10} \, _2F_1\left (\frac{5}{2},4;\frac{7}{2};\frac{b x^4}{a}+1\right )\right )+10 a^5 f x \, _2F_1\left (-\frac{9}{4},-\frac{3}{2};-\frac{5}{4};-\frac{b x^4}{a}\right )\right )+90 a^5 d \, _2F_1\left (-\frac{11}{4},-\frac{3}{2};-\frac{7}{4};-\frac{b x^4}{a}\right )\right )}{990 a^4 x^{11} \sqrt{\frac{b x^4}{a}+1}} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.023, size = 462, normalized size = 1. \begin{align*} -{\frac{ad}{11\,{x}^{11}}\sqrt{b{x}^{4}+a}}-{\frac{13\,bd}{77\,{x}^{7}}\sqrt{b{x}^{4}+a}}-{\frac{4\,{b}^{2}d}{77\,a{x}^{3}}\sqrt{b{x}^{4}+a}}-{\frac{4\,{b}^{3}d}{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{e \left ({b}^{2}{x}^{8}+2\,ab{x}^{4}+{a}^{2} \right ) }{10\,{x}^{10}a}\sqrt{b{x}^{4}+a}}-{\frac{7\,bc}{48\,{x}^{8}}\sqrt{b{x}^{4}+a}}-{\frac{{b}^{2}c}{32\,a{x}^{4}}\sqrt{b{x}^{4}+a}}+{\frac{{b}^{3}c}{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{ac}{12\,{x}^{12}}\sqrt{b{x}^{4}+a}}-{\frac{af}{9\,{x}^{9}}\sqrt{b{x}^{4}+a}}-{\frac{11\,fb}{45\,{x}^{5}}\sqrt{b{x}^{4}+a}}-{\frac{4\,{b}^{2}f}{15\,ax}\sqrt{b{x}^{4}+a}}+{{\frac{4\,i}{15}}f{b}^{{\frac{5}{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 ){\frac{1}{\sqrt{a}}}{\frac{1}{\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}}}}{\frac{1}{\sqrt{b{x}^{4}+a}}}}-{{\frac{4\,i}{15}}f{b}^{{\frac{5}{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 ){\frac{1}{\sqrt{a}}}{\frac{1}{\sqrt{{i\sqrt{b}{\frac{1}{\sqrt{a}}}}}}}{\frac{1}{\sqrt{b{x}^{4}+a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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^{13}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 20.1769, size = 403, normalized size = 0.9 \begin{align*} \frac{a^{\frac{3}{2}} d \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{a^{\frac{3}{2}} f \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 d \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{\sqrt{a} b f \Gamma \left (- \frac{5}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{4 x^{5} \Gamma \left (- \frac{1}{4}\right )} - \frac{a^{2} c}{12 \sqrt{b} x^{14} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{11 a \sqrt{b} c}{48 x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{17 b^{\frac{3}{2}} c}{96 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{5}{2}} c}{32 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} + \frac{b^{3} c \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^{13}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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