Optimal. Leaf size=452 \[ \frac {4 a^2 d x \sqrt {a+b x^4}}{77 b}-\frac {a^2 e x^2 \sqrt {a+b x^4}}{32 b}+\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}-\frac {4 a^3 f x \sqrt {a+b x^4}}{65 b^{3/2} \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}-\frac {a^3 e \tanh ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a+b x^4}}\right )}{32 b^{3/2}}+\frac {4 a^{13/4} f \left (\sqrt {a}+\sqrt {b} x^2\right ) \sqrt {\frac {a+b x^4}{\left (\sqrt {a}+\sqrt {b} x^2\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{65 b^{7/4} \sqrt {a+b x^4}}-\frac {2 a^{11/4} \left (65 \sqrt {b} d+77 \sqrt {a} f\right ) \left (\sqrt {a}+\sqrt {b} x^2\right ) \sqrt {\frac {a+b x^4}{\left (\sqrt {a}+\sqrt {b} x^2\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{5005 b^{7/4} \sqrt {a+b x^4}} \]
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Rubi [A]
time = 0.29, antiderivative size = 452, normalized size of antiderivative = 1.00, number of steps
used = 15, number of rules used = 11, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.367, Rules used = {1847, 1266,
794, 201, 223, 212, 1288, 1294, 1212, 226, 1210} \begin {gather*} -\frac {2 a^{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 (77 \sqrt {a} f+65 \sqrt {b} d\right ) F\left (2 \text {ArcTan}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{5005 b^{7/4} \sqrt {a+b x^4}}+\frac {4 a^{13/4} 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 \text {ArcTan}\left (\frac {\sqrt [4]{b} x}{\sqrt [4]{a}}\right )|\frac {1}{2}\right )}{65 b^{7/4} \sqrt {a+b x^4}}-\frac {a^3 e \tanh ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a+b x^4}}\right )}{32 b^{3/2}}-\frac {4 a^3 f x \sqrt {a+b x^4}}{65 b^{3/2} \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {4 a^2 d x \sqrt {a+b x^4}}{77 b}-\frac {a^2 e x^2 \sqrt {a+b x^4}}{32 b}+\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}+\frac {\left (a+b x^4\right )^{5/2} \left (6 c+5 e x^2\right )}{60 b}+\frac {1}{143} x^5 \left (a+b x^4\right )^{3/2} \left (13 d+11 f x^2\right )+\frac {2 a x^5 \sqrt {a+b x^4} \left (117 d+77 f x^2\right )}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 201
Rule 212
Rule 223
Rule 226
Rule 794
Rule 1210
Rule 1212
Rule 1266
Rule 1288
Rule 1294
Rule 1847
Rubi steps
\begin {align*} \int x^3 \left (c+d x+e x^2+f x^3\right ) \left (a+b x^4\right )^{3/2} \, dx &=\int \left (x^3 \left (c+e x^2\right ) \left (a+b x^4\right )^{3/2}+x^4 \left (d+f x^2\right ) \left (a+b x^4\right )^{3/2}\right ) \, dx\\ &=\int x^3 \left (c+e x^2\right ) \left (a+b x^4\right )^{3/2} \, dx+\int x^4 \left (d+f x^2\right ) \left (a+b x^4\right )^{3/2} \, dx\\ &=\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {1}{2} \text {Subst}\left (\int x (c+e x) \left (a+b x^2\right )^{3/2} \, dx,x,x^2\right )+\frac {1}{143} (6 a) \int x^4 \left (13 d+11 f x^2\right ) \sqrt {a+b x^4} \, dx\\ &=\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}+\frac {\left (4 a^2\right ) \int \frac {x^4 \left (117 d+77 f x^2\right )}{\sqrt {a+b x^4}} \, dx}{3003}-\frac {(a e) \text {Subst}\left (\int \left (a+b x^2\right )^{3/2} \, dx,x,x^2\right )}{12 b}\\ &=\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}+\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}-\frac {\left (4 a^2\right ) \int \frac {x^2 \left (231 a f-585 b d x^2\right )}{\sqrt {a+b x^4}} \, dx}{15015 b}-\frac {\left (a^2 e\right ) \text {Subst}\left (\int \sqrt {a+b x^2} \, dx,x,x^2\right )}{16 b}\\ &=\frac {4 a^2 d x \sqrt {a+b x^4}}{77 b}-\frac {a^2 e x^2 \sqrt {a+b x^4}}{32 b}+\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}+\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}+\frac {\left (4 a^2\right ) \int \frac {-585 a b d-693 a b f x^2}{\sqrt {a+b x^4}} \, dx}{45045 b^2}-\frac {\left (a^3 e\right ) \text {Subst}\left (\int \frac {1}{\sqrt {a+b x^2}} \, dx,x,x^2\right )}{32 b}\\ &=\frac {4 a^2 d x \sqrt {a+b x^4}}{77 b}-\frac {a^2 e x^2 \sqrt {a+b x^4}}{32 b}+\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}+\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}-\frac {\left (a^3 e\right ) \text {Subst}\left (\int \frac {1}{1-b x^2} \, dx,x,\frac {x^2}{\sqrt {a+b x^4}}\right )}{32 b}+\frac {\left (4 a^{7/2} f\right ) \int \frac {1-\frac {\sqrt {b} x^2}{\sqrt {a}}}{\sqrt {a+b x^4}} \, dx}{65 b^{3/2}}-\frac {\left (4 a^3 \left (65 \sqrt {b} d+77 \sqrt {a} f\right )\right ) \int \frac {1}{\sqrt {a+b x^4}} \, dx}{5005 b^{3/2}}\\ &=\frac {4 a^2 d x \sqrt {a+b x^4}}{77 b}-\frac {a^2 e x^2 \sqrt {a+b x^4}}{32 b}+\frac {4 a^2 f x^3 \sqrt {a+b x^4}}{195 b}-\frac {4 a^3 f x \sqrt {a+b x^4}}{65 b^{3/2} \left (\sqrt {a}+\sqrt {b} x^2\right )}+\frac {2 a x^5 \left (117 d+77 f x^2\right ) \sqrt {a+b x^4}}{3003}-\frac {a e x^2 \left (a+b x^4\right )^{3/2}}{48 b}+\frac {1}{143} x^5 \left (13 d+11 f x^2\right ) \left (a+b x^4\right )^{3/2}+\frac {\left (6 c+5 e x^2\right ) \left (a+b x^4\right )^{5/2}}{60 b}-\frac {a^3 e \tanh ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a+b x^4}}\right )}{32 b^{3/2}}+\frac {4 a^{13/4} 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 )}{65 b^{7/4} \sqrt {a+b x^4}}-\frac {2 a^{11/4} \left (65 \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 )}{5005 b^{7/4} \sqrt {a+b x^4}}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 5 vs. order 4 in
optimal.
time = 10.45, size = 238, normalized size = 0.53 \begin {gather*} \frac {\sqrt {a+b x^4} \left (6864 \sqrt {b} c \left (a+b x^4\right )^2+6240 \sqrt {b} d x \left (a+b x^4\right )^2+5280 \sqrt {b} f x^3 \left (a+b x^4\right )^2+715 e \left (\sqrt {b} x^2 \left (3 a^2+14 a b x^4+8 b^2 x^8\right )-\frac {3 a^{5/2} \sinh ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{\sqrt {1+\frac {b x^4}{a}}}\right )-\frac {6240 a^2 \sqrt {b} d x \, _2F_1\left (-\frac {3}{2},\frac {1}{4};\frac {5}{4};-\frac {b x^4}{a}\right )}{\sqrt {1+\frac {b x^4}{a}}}-\frac {5280 a^2 \sqrt {b} f x^3 \, _2F_1\left (-\frac {3}{2},\frac {3}{4};\frac {7}{4};-\frac {b x^4}{a}\right )}{\sqrt {1+\frac {b x^4}{a}}}\right )}{68640 b^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains complex when optimal does not.
time = 0.37, size = 372, normalized size = 0.82
method | result | size |
default | \(f \left (\frac {b \,x^{11} \sqrt {b \,x^{4}+a}}{13}+\frac {5 a \,x^{7} \sqrt {b \,x^{4}+a}}{39}+\frac {4 a^{2} x^{3} \sqrt {b \,x^{4}+a}}{195 b}-\frac {4 i a^{\frac {7}{2}} \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \left (\EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )-\EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )\right )}{65 b^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\right )+e \left (\frac {b \,x^{10} \sqrt {b \,x^{4}+a}}{12}+\frac {7 a \,x^{6} \sqrt {b \,x^{4}+a}}{48}+\frac {a^{2} x^{2} \sqrt {b \,x^{4}+a}}{32 b}-\frac {a^{3} \ln \left (x^{2} \sqrt {b}+\sqrt {b \,x^{4}+a}\right )}{32 b^{\frac {3}{2}}}\right )+d \left (\frac {b \,x^{9} \sqrt {b \,x^{4}+a}}{11}+\frac {13 a \,x^{5} \sqrt {b \,x^{4}+a}}{77}+\frac {4 a^{2} x \sqrt {b \,x^{4}+a}}{77 b}-\frac {4 a^{3} \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{77 b \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\right )+\frac {c \left (b \,x^{4}+a \right )^{\frac {5}{2}}}{10 b}\) | \(372\) |
risch | \(\frac {\left (36960 b^{2} f \,x^{11}+40040 b^{2} e \,x^{10}+43680 b^{2} d \,x^{9}+48048 b^{2} c \,x^{8}+61600 a b f \,x^{7}+70070 a b e \,x^{6}+81120 a b d \,x^{5}+96096 a b c \,x^{4}+9856 a^{2} f \,x^{3}+15015 a^{2} e \,x^{2}+24960 a^{2} d x +48048 a^{2} c \right ) \sqrt {b \,x^{4}+a}}{480480 b}-\frac {4 i a^{\frac {7}{2}} f \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{65 b^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}+\frac {4 i a^{\frac {7}{2}} f \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{65 b^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}-\frac {a^{3} e \ln \left (x^{2} \sqrt {b}+\sqrt {b \,x^{4}+a}\right )}{32 b^{\frac {3}{2}}}-\frac {4 a^{3} d \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{77 b \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\) | \(376\) |
elliptic | \(\frac {b f \,x^{11} \sqrt {b \,x^{4}+a}}{13}+\frac {b e \,x^{10} \sqrt {b \,x^{4}+a}}{12}+\frac {b d \,x^{9} \sqrt {b \,x^{4}+a}}{11}+\frac {b c \,x^{8} \sqrt {b \,x^{4}+a}}{10}+\frac {5 a f \,x^{7} \sqrt {b \,x^{4}+a}}{39}+\frac {7 a e \,x^{6} \sqrt {b \,x^{4}+a}}{48}+\frac {13 a d \,x^{5} \sqrt {b \,x^{4}+a}}{77}+\frac {a c \,x^{4} \sqrt {b \,x^{4}+a}}{5}+\frac {4 a^{2} f \,x^{3} \sqrt {b \,x^{4}+a}}{195 b}+\frac {a^{2} e \,x^{2} \sqrt {b \,x^{4}+a}}{32 b}+\frac {4 a^{2} d x \sqrt {b \,x^{4}+a}}{77 b}+\frac {a^{2} c \sqrt {b \,x^{4}+a}}{10 b}-\frac {4 a^{3} d \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )}{77 b \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}-\frac {a^{3} e \ln \left (2 x^{2} \sqrt {b}+2 \sqrt {b \,x^{4}+a}\right )}{32 b^{\frac {3}{2}}}-\frac {4 i a^{\frac {7}{2}} f \sqrt {1-\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \sqrt {1+\frac {i \sqrt {b}\, x^{2}}{\sqrt {a}}}\, \left (\EllipticF \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )-\EllipticE \left (x \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}, i\right )\right )}{65 b^{\frac {3}{2}} \sqrt {\frac {i \sqrt {b}}{\sqrt {a}}}\, \sqrt {b \,x^{4}+a}}\) | \(413\) |
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 = 0.12, size = 255, normalized size = 0.56 \begin {gather*} -\frac {59136 \, a^{3} \sqrt {b} f x \left (-\frac {a}{b}\right )^{\frac {3}{4}} E(\arcsin \left (\frac {\left (-\frac {a}{b}\right )^{\frac {1}{4}}}{x}\right )\,|\,-1) - 15015 \, a^{3} \sqrt {b} e x \log \left (-2 \, b x^{4} + 2 \, \sqrt {b x^{4} + a} \sqrt {b} x^{2} - a\right ) + 768 \, {\left (65 \, a^{2} b d - 77 \, a^{3} f\right )} \sqrt {b} x \left (-\frac {a}{b}\right )^{\frac {3}{4}} F(\arcsin \left (\frac {\left (-\frac {a}{b}\right )^{\frac {1}{4}}}{x}\right )\,|\,-1) - 2 \, {\left (36960 \, b^{3} f x^{12} + 40040 \, b^{3} e x^{11} + 43680 \, b^{3} d x^{10} + 48048 \, b^{3} c x^{9} + 61600 \, a b^{2} f x^{8} + 70070 \, a b^{2} e x^{7} + 81120 \, a b^{2} d x^{6} + 96096 \, a b^{2} c x^{5} + 9856 \, a^{2} b f x^{4} + 15015 \, a^{2} b e x^{3} + 24960 \, a^{2} b d x^{2} + 48048 \, a^{2} b c x - 29568 \, a^{3} f\right )} \sqrt {b x^{4} + a}}{960960 \, b^{2} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 9.94, size = 398, normalized size = 0.88 \begin {gather*} \frac {a^{\frac {5}{2}} e x^{2}}{32 b \sqrt {1 + \frac {b x^{4}}{a}}} + \frac {a^{\frac {3}{2}} d x^{5} \Gamma \left (\frac {5}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2}, \frac {5}{4} \\ \frac {9}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 \Gamma \left (\frac {9}{4}\right )} + \frac {17 a^{\frac {3}{2}} e x^{6}}{96 \sqrt {1 + \frac {b x^{4}}{a}}} + \frac {a^{\frac {3}{2}} f x^{7} \Gamma \left (\frac {7}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2}, \frac {7}{4} \\ \frac {11}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 \Gamma \left (\frac {11}{4}\right )} + \frac {\sqrt {a} b d x^{9} \Gamma \left (\frac {9}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2}, \frac {9}{4} \\ \frac {13}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 \Gamma \left (\frac {13}{4}\right )} + \frac {11 \sqrt {a} b e x^{10}}{48 \sqrt {1 + \frac {b x^{4}}{a}}} + \frac {\sqrt {a} b f x^{11} \Gamma \left (\frac {11}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2}, \frac {11}{4} \\ \frac {15}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 \Gamma \left (\frac {15}{4}\right )} - \frac {a^{3} e \operatorname {asinh}{\left (\frac {\sqrt {b} x^{2}}{\sqrt {a}} \right )}}{32 b^{\frac {3}{2}}} + a c \left (\begin {cases} \frac {\sqrt {a} x^{4}}{4} & \text {for}\: b = 0 \\\frac {\left (a + b x^{4}\right )^{\frac {3}{2}}}{6 b} & \text {otherwise} \end {cases}\right ) + b c \left (\begin {cases} - \frac {a^{2} \sqrt {a + b x^{4}}}{15 b^{2}} + \frac {a x^{4} \sqrt {a + b x^{4}}}{30 b} + \frac {x^{8} \sqrt {a + b x^{4}}}{10} & \text {for}\: b \neq 0 \\\frac {\sqrt {a} x^{8}}{8} & \text {otherwise} \end {cases}\right ) + \frac {b^{2} e x^{14}}{12 \sqrt {a} \sqrt {1 + \frac {b x^{4}}{a}}} \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 x^3\,{\left (b\,x^4+a\right )}^{3/2}\,\left (f\,x^3+e\,x^2+d\,x+c\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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