Optimal. Leaf size=425 \[ -\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}-\frac {2 b^{5/2} c x \sqrt {a+b x^4}}{15 a^2 \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {b^2 d \tanh ^{-1}\left (\frac {\sqrt {a+b x^4}}{\sqrt {a}}\right )}{16 a^{3/2}}+\frac {2 b^{9/4} c \left (\sqrt {a}+\sqrt {b} x^2\right ) \sqrt {\frac {a+b x^4}{\left (\sqrt {a}+\sqrt {b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{15 a^{7/4} \sqrt {a+b x^4}}-\frac {b^{7/4} \left (7 \sqrt {b} c+5 \sqrt {a} e\right ) \left (\sqrt {a}+\sqrt {b} x^2\right ) \sqrt {\frac {a+b x^4}{\left (\sqrt {a}+\sqrt {b} x^2\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{105 a^{7/4} \sqrt {a+b x^4}} \]
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Rubi [A]
time = 0.30, antiderivative size = 425, normalized size of antiderivative = 1.00, 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, 1839,
1847, 1296, 1212, 226, 1210, 1266, 849, 821, 272, 65, 214} \begin {gather*} -\frac {b^{7/4} \left (\sqrt {a}+\sqrt {b} x^2\right ) \sqrt {\frac {a+b x^4}{\left (\sqrt {a}+\sqrt {b} x^2\right )^2}} \left (5 \sqrt {a} e+7 \sqrt {b} c\right ) F\left (2 \text {ArcTan}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{105 a^{7/4} \sqrt {a+b x^4}}+\frac {2 b^{9/4} 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 \text {ArcTan}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{15 a^{7/4} \sqrt {a+b x^4}}+\frac {b^2 d \tanh ^{-1}\left (\frac {\sqrt {a+b x^4}}{\sqrt {a}}\right )}{16 a^{3/2}}-\frac {2 b^{5/2} c x \sqrt {a+b x^4}}{15 a^2 \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}-\frac {1}{504} \sqrt {a+b x^4} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right )-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 65
Rule 214
Rule 226
Rule 272
Rule 821
Rule 849
Rule 1210
Rule 1212
Rule 1266
Rule 1296
Rule 1839
Rule 1847
Rubi steps
\begin {align*} \int \frac {\left (c+d x+e x^2+f x^3\right ) \sqrt {a+b x^4}}{x^{10}} \, dx &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-(2 b) \int \frac {-\frac {c}{9}-\frac {d x}{8}-\frac {e x^2}{7}-\frac {f x^3}{6}}{x^6 \sqrt {a+b x^4}} \, dx\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-(2 b) \int \left (\frac {-\frac {c}{9}-\frac {e x^2}{7}}{x^6 \sqrt {a+b x^4}}+\frac {-\frac {d}{8}-\frac {f x^2}{6}}{x^5 \sqrt {a+b x^4}}\right ) \, dx\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-(2 b) \int \frac {-\frac {c}{9}-\frac {e x^2}{7}}{x^6 \sqrt {a+b x^4}} \, dx-(2 b) \int \frac {-\frac {d}{8}-\frac {f x^2}{6}}{x^5 \sqrt {a+b x^4}} \, dx\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-b \text {Subst}\left (\int \frac {-\frac {d}{8}-\frac {f x}{6}}{x^3 \sqrt {a+b x^2}} \, dx,x,x^2\right )+\frac {(2 b) \int \frac {\frac {5 a e}{7}-\frac {1}{3} b c x^2}{x^4 \sqrt {a+b x^4}} \, dx}{5 a}\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {(2 b) \int \frac {a b c+\frac {5}{7} a b e x^2}{x^2 \sqrt {a+b x^4}} \, dx}{15 a^2}+\frac {b \text {Subst}\left (\int \frac {\frac {a f}{3}-\frac {b d x}{8}}{x^2 \sqrt {a+b x^2}} \, dx,x,x^2\right )}{2 a}\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}+\frac {(2 b) \int \frac {-\frac {5}{7} a^2 b e-a b^2 c x^2}{\sqrt {a+b x^4}} \, dx}{15 a^3}-\frac {\left (b^2 d\right ) \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x^2}} \, dx,x,x^2\right )}{16 a}\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}+\frac {\left (2 b^{5/2} c\right ) \int \frac {1-\frac {\sqrt {b} x^2}{\sqrt {a}}}{\sqrt {a+b x^4}} \, dx}{15 a^{3/2}}-\frac {\left (b^2 d\right ) \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,x^4\right )}{32 a}-\frac {\left (2 b^2 \left (7 \sqrt {b} c+5 \sqrt {a} e\right )\right ) \int \frac {1}{\sqrt {a+b x^4}} \, dx}{105 a^{3/2}}\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}-\frac {2 b^{5/2} c x \sqrt {a+b x^4}}{15 a^2 \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {2 b^{9/4} 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 )}{15 a^{7/4} \sqrt {a+b x^4}}-\frac {b^{7/4} \left (7 \sqrt {b} c+5 \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 )}{105 a^{7/4} \sqrt {a+b x^4}}-\frac {(b d) \text {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b x^4}\right )}{16 a}\\ &=-\frac {1}{504} \left (\frac {56 c}{x^9}+\frac {63 d}{x^8}+\frac {72 e}{x^7}+\frac {84 f}{x^6}\right ) \sqrt {a+b x^4}-\frac {2 b c \sqrt {a+b x^4}}{45 a x^5}-\frac {b d \sqrt {a+b x^4}}{16 a x^4}-\frac {2 b e \sqrt {a+b x^4}}{21 a x^3}-\frac {b f \sqrt {a+b x^4}}{6 a x^2}+\frac {2 b^2 c \sqrt {a+b x^4}}{15 a^2 x}-\frac {2 b^{5/2} c x \sqrt {a+b x^4}}{15 a^2 \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {b^2 d \tanh ^{-1}\left (\frac {\sqrt {a+b x^4}}{\sqrt {a}}\right )}{16 a^{3/2}}+\frac {2 b^{9/4} 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 )}{15 a^{7/4} \sqrt {a+b x^4}}-\frac {b^{7/4} \left (7 \sqrt {b} c+5 \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 )}{105 a^{7/4} \sqrt {a+b x^4}}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 10.38, size = 305, normalized size = 0.72 \begin {gather*} \frac {\sqrt {\frac {i \sqrt {b}}{\sqrt {a}}} \left (-\left (\left (a+b x^4\right ) \left (-672 b^2 c x^8+10 a^2 \left (56 c+63 d x+72 e x^2+84 f x^3\right )+a b x^4 (224 c+15 x (21 d+8 x (4 e+7 f x)))\right )\right )+315 \sqrt {a} b^2 d x^9 \sqrt {a+b x^4} \tanh ^{-1}\left (\frac {\sqrt {a+b x^4}}{\sqrt {a}}\right )\right )-672 \sqrt {a} b^{5/2} c x^9 \sqrt {1+\frac {b x^4}{a}} E\left (\left .i \sinh ^{-1}\left (\sqrt {\frac {i \sqrt {b}}{\sqrt {a}}} x\right )\right |-1\right )+96 \sqrt {a} b^2 \left (7 \sqrt {b} c+5 i \sqrt {a} e\right ) x^9 \sqrt {1+\frac {b x^4}{a}} F\left (\left .i \sinh ^{-1}\left (\sqrt {\frac {i \sqrt {b}}{\sqrt {a}}} x\right )\right |-1\right )}{5040 a^2 \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}} x^9 \sqrt {a+b x^4}} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains complex when optimal does not.
time = 0.42, size = 368, normalized size = 0.87
method | result | size |
elliptic | \(-\frac {c \sqrt {b \,x^{4}+a}}{9 x^{9}}-\frac {d \sqrt {b \,x^{4}+a}}{8 x^{8}}-\frac {e \sqrt {b \,x^{4}+a}}{7 x^{7}}-\frac {f \sqrt {b \,x^{4}+a}}{6 x^{6}}-\frac {2 b c \sqrt {b \,x^{4}+a}}{45 a \,x^{5}}-\frac {b d \sqrt {b \,x^{4}+a}}{16 a \,x^{4}}-\frac {2 b e \sqrt {b \,x^{4}+a}}{21 a \,x^{3}}-\frac {b f \sqrt {b \,x^{4}+a}}{6 a \,x^{2}}+\frac {2 b^{2} c \sqrt {b \,x^{4}+a}}{15 a^{2} x}-\frac {2 b^{2} e \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{21 a \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}-\frac {2 i b^{\frac {5}{2}} c \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \left (\EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )-\EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )\right )}{15 a^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}+\frac {b^{2} d \arctanh \left (\frac {\sqrt {a}}{\sqrt {b \,x^{4}+a}}\right )}{16 a^{\frac {3}{2}}}\) | \(356\) |
risch | \(-\frac {\sqrt {b \,x^{4}+a}\, \left (-672 b^{2} c \,x^{8}+840 a b f \,x^{7}+480 a b e \,x^{6}+315 a b d \,x^{5}+224 a b c \,x^{4}+840 a^{2} f \,x^{3}+720 a^{2} e \,x^{2}+630 a^{2} d x +560 a^{2} c \right )}{5040 x^{9} a^{2}}-\frac {2 i b^{\frac {5}{2}} c \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{15 a^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}+\frac {2 i b^{\frac {5}{2}} c \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{15 a^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}-\frac {2 b^{2} e \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{21 a \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}+\frac {b^{2} d \ln \left (\frac {2 a +2 \sqrt {a}\, \sqrt {b \,x^{4}+a}}{x^{2}}\right )}{16 a^{\frac {3}{2}}}\) | \(357\) |
default | \(c \left (-\frac {\sqrt {b \,x^{4}+a}}{9 x^{9}}-\frac {2 b \sqrt {b \,x^{4}+a}}{45 a \,x^{5}}+\frac {2 b^{2} \sqrt {b \,x^{4}+a}}{15 a^{2} x}-\frac {2 i b^{\frac {5}{2}} \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \left (\EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )-\EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )\right )}{15 a^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\right )-\frac {f \left (b \,x^{4}+a \right )^{\frac {3}{2}}}{6 a \,x^{6}}+d \left (-\frac {\left (b \,x^{4}+a \right )^{\frac {3}{2}}}{8 a \,x^{8}}+\frac {b \left (b \,x^{4}+a \right )^{\frac {3}{2}}}{16 a^{2} x^{4}}+\frac {b^{2} \ln \left (\frac {2 a +2 \sqrt {a}\, \sqrt {b \,x^{4}+a}}{x^{2}}\right )}{16 a^{\frac {3}{2}}}-\frac {b^{2} \sqrt {b \,x^{4}+a}}{16 a^{2}}\right )+e \left (-\frac {\sqrt {b \,x^{4}+a}}{7 x^{7}}-\frac {2 b \sqrt {b \,x^{4}+a}}{21 a \,x^{3}}-\frac {2 b^{2} \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{21 a \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\right )\) | \(368\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.13, size = 208, normalized size = 0.49 \begin {gather*} \frac {1344 \, \sqrt {a} b^{2} c x^{9} \left (-\frac {b}{a}\right )^{\frac {3}{4}} E(\arcsin \left (x \left (-\frac {b}{a}\right )^{\frac {1}{4}}\right )\,|\,-1) + 315 \, \sqrt {a} b^{2} d x^{9} \log \left (-\frac {b x^{4} + 2 \, \sqrt {b x^{4} + a} \sqrt {a} + 2 \, a}{x^{4}}\right ) - 192 \, {\left (7 \, b^{2} c - 5 \, a b e\right )} \sqrt {a} x^{9} \left (-\frac {b}{a}\right )^{\frac {3}{4}} F(\arcsin \left (x \left (-\frac {b}{a}\right )^{\frac {1}{4}}\right )\,|\,-1) + 2 \, {\left (672 \, b^{2} c x^{8} - 840 \, a b f x^{7} - 480 \, a b e x^{6} - 315 \, a b d x^{5} - 224 \, a b c x^{4} - 840 \, a^{2} f x^{3} - 720 \, a^{2} e x^{2} - 630 \, a^{2} d x - 560 \, a^{2} c\right )} \sqrt {b x^{4} + a}}{10080 \, a^{2} x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] Result contains complex when optimal does not.
time = 4.47, size = 246, normalized size = 0.58 \begin {gather*} \frac {\sqrt {a} 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} 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 d}{8 \sqrt {b} x^{10} \sqrt {\frac {a}{b x^{4}} + 1}} - \frac {3 \sqrt {b} d}{16 x^{6} \sqrt {\frac {a}{b x^{4}} + 1}} - \frac {\sqrt {b} f \sqrt {\frac {a}{b x^{4}} + 1}}{6 x^{4}} - \frac {b^{\frac {3}{2}} d}{16 a x^{2} \sqrt {\frac {a}{b x^{4}} + 1}} - \frac {b^{\frac {3}{2}} f \sqrt {\frac {a}{b x^{4}} + 1}}{6 a} + \frac {b^{2} d \operatorname {asinh}{\left (\frac {\sqrt {a}}{\sqrt {b} x^{2}} \right )}}{16 a^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {b\,x^4+a}\,\left (f\,x^3+e\,x^2+d\,x+c\right )}{x^{10}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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