Optimal. Leaf size=264 \[ -\frac {5 b^2 (b+2 c x) \left (b x+c x^2\right )^{3/2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{6144 c^4}+\frac {(b+2 c x) \left (b x+c x^2\right )^{5/2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{384 c^3}-\frac {5 b^6 \tanh ^{-1}\left (\frac {\sqrt {c} x}{\sqrt {b x+c x^2}}\right ) \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{16384 c^{11/2}}+\frac {5 b^4 (b+2 c x) \sqrt {b x+c x^2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{16384 c^5}-\frac {\left (b x+c x^2\right )^{7/2} (-16 c (A e+B d)+9 b B e-14 B c e x)}{112 c^2} \]
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Rubi [A] time = 0.25, antiderivative size = 264, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {779, 612, 620, 206} \begin {gather*} \frac {5 b^4 (b+2 c x) \sqrt {b x+c x^2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{16384 c^5}-\frac {5 b^2 (b+2 c x) \left (b x+c x^2\right )^{3/2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{6144 c^4}+\frac {(b+2 c x) \left (b x+c x^2\right )^{5/2} \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{384 c^3}-\frac {5 b^6 \tanh ^{-1}\left (\frac {\sqrt {c} x}{\sqrt {b x+c x^2}}\right ) \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{16384 c^{11/2}}-\frac {\left (b x+c x^2\right )^{7/2} (-16 c (A e+B d)+9 b B e-14 B c e x)}{112 c^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 206
Rule 612
Rule 620
Rule 779
Rubi steps
\begin {align*} \int (A+B x) (d+e x) \left (b x+c x^2\right )^{5/2} \, dx &=-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}+\frac {\left (\frac {9}{2} b^2 B e+8 c (2 A c d-b (B d+A e))\right ) \int \left (b x+c x^2\right )^{5/2} \, dx}{16 c^2}\\ &=\frac {\left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{5/2}}{384 c^3}-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}-\frac {\left (5 b^2 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right )\right ) \int \left (b x+c x^2\right )^{3/2} \, dx}{768 c^3}\\ &=-\frac {5 b^2 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{3/2}}{6144 c^4}+\frac {\left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{5/2}}{384 c^3}-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}+\frac {\left (5 b^4 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right )\right ) \int \sqrt {b x+c x^2} \, dx}{4096 c^4}\\ &=\frac {5 b^4 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \sqrt {b x+c x^2}}{16384 c^5}-\frac {5 b^2 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{3/2}}{6144 c^4}+\frac {\left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{5/2}}{384 c^3}-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}-\frac {\left (5 b^6 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right )\right ) \int \frac {1}{\sqrt {b x+c x^2}} \, dx}{32768 c^5}\\ &=\frac {5 b^4 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \sqrt {b x+c x^2}}{16384 c^5}-\frac {5 b^2 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{3/2}}{6144 c^4}+\frac {\left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{5/2}}{384 c^3}-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}-\frac {\left (5 b^6 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right )\right ) \operatorname {Subst}\left (\int \frac {1}{1-c x^2} \, dx,x,\frac {x}{\sqrt {b x+c x^2}}\right )}{16384 c^5}\\ &=\frac {5 b^4 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \sqrt {b x+c x^2}}{16384 c^5}-\frac {5 b^2 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{3/2}}{6144 c^4}+\frac {\left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) (b+2 c x) \left (b x+c x^2\right )^{5/2}}{384 c^3}-\frac {(9 b B e-16 c (B d+A e)-14 B c e x) \left (b x+c x^2\right )^{7/2}}{112 c^2}-\frac {5 b^6 \left (32 A c^2 d+9 b^2 B e-16 b c (B d+A e)\right ) \tanh ^{-1}\left (\frac {\sqrt {c} x}{\sqrt {b x+c x^2}}\right )}{16384 c^{11/2}}\\ \end {align*}
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Mathematica [A] time = 0.80, size = 315, normalized size = 1.19 \begin {gather*} \frac {\sqrt {x (b+c x)} \left (\sqrt {c} \left (-210 b^6 c (8 A e+8 B d+3 B e x)+56 b^5 c^2 (20 A (3 d+e x)+B x (20 d+9 e x))-16 b^4 c^3 x (28 A (5 d+2 e x)+B x (56 d+27 e x))+128 b^3 c^4 x^2 (2 A (7 d+3 e x)+3 B x (2 d+e x))+256 b^2 c^5 x^3 (A (378 d+296 e x)+B x (296 d+243 e x))+1024 b c^6 x^4 (4 A (35 d+29 e x)+B x (116 d+99 e x))+2048 c^7 x^5 (4 A (7 d+6 e x)+3 B x (8 d+7 e x))+945 b^7 B e\right )-\frac {105 b^{11/2} \sinh ^{-1}\left (\frac {\sqrt {c} \sqrt {x}}{\sqrt {b}}\right ) \left (-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right )}{\sqrt {x} \sqrt {\frac {c x}{b}+1}}\right )}{344064 c^{11/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 1.76, size = 407, normalized size = 1.54 \begin {gather*} \frac {5 \log \left (-2 \sqrt {c} \sqrt {b x+c x^2}+b+2 c x\right ) \left (-16 A b^7 c e+32 A b^6 c^2 d+9 b^8 B e-16 b^7 B c d\right )}{32768 c^{11/2}}+\frac {\sqrt {b x+c x^2} \left (-1680 A b^6 c e+3360 A b^5 c^2 d+1120 A b^5 c^2 e x-2240 A b^4 c^3 d x-896 A b^4 c^3 e x^2+1792 A b^3 c^4 d x^2+768 A b^3 c^4 e x^3+96768 A b^2 c^5 d x^3+75776 A b^2 c^5 e x^4+143360 A b c^6 d x^4+118784 A b c^6 e x^5+57344 A c^7 d x^5+49152 A c^7 e x^6+945 b^7 B e-1680 b^6 B c d-630 b^6 B c e x+1120 b^5 B c^2 d x+504 b^5 B c^2 e x^2-896 b^4 B c^3 d x^2-432 b^4 B c^3 e x^3+768 b^3 B c^4 d x^3+384 b^3 B c^4 e x^4+75776 b^2 B c^5 d x^4+62208 b^2 B c^5 e x^5+118784 b B c^6 d x^5+101376 b B c^6 e x^6+49152 B c^7 d x^6+43008 B c^7 e x^7\right )}{344064 c^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 802, normalized size = 3.04 \begin {gather*} \left [\frac {105 \, {\left (16 \, {\left (B b^{7} c - 2 \, A b^{6} c^{2}\right )} d - {\left (9 \, B b^{8} - 16 \, A b^{7} c\right )} e\right )} \sqrt {c} \log \left (2 \, c x + b + 2 \, \sqrt {c x^{2} + b x} \sqrt {c}\right ) + 2 \, {\left (43008 \, B c^{8} e x^{7} + 3072 \, {\left (16 \, B c^{8} d + {\left (33 \, B b c^{7} + 16 \, A c^{8}\right )} e\right )} x^{6} + 256 \, {\left (16 \, {\left (29 \, B b c^{7} + 14 \, A c^{8}\right )} d + {\left (243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right )} e\right )} x^{5} + 128 \, {\left (16 \, {\left (37 \, B b^{2} c^{6} + 70 \, A b c^{7}\right )} d + {\left (3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right )} e\right )} x^{4} + 48 \, {\left (16 \, {\left (B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right )} d - {\left (9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right )} e\right )} x^{3} - 56 \, {\left (16 \, {\left (B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right )} d - {\left (9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right )} e\right )} x^{2} - 1680 \, {\left (B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right )} d + 105 \, {\left (9 \, B b^{7} c - 16 \, A b^{6} c^{2}\right )} e + 70 \, {\left (16 \, {\left (B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right )} d - {\left (9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right )} e\right )} x\right )} \sqrt {c x^{2} + b x}}{688128 \, c^{6}}, -\frac {105 \, {\left (16 \, {\left (B b^{7} c - 2 \, A b^{6} c^{2}\right )} d - {\left (9 \, B b^{8} - 16 \, A b^{7} c\right )} e\right )} \sqrt {-c} \arctan \left (\frac {\sqrt {c x^{2} + b x} \sqrt {-c}}{c x}\right ) - {\left (43008 \, B c^{8} e x^{7} + 3072 \, {\left (16 \, B c^{8} d + {\left (33 \, B b c^{7} + 16 \, A c^{8}\right )} e\right )} x^{6} + 256 \, {\left (16 \, {\left (29 \, B b c^{7} + 14 \, A c^{8}\right )} d + {\left (243 \, B b^{2} c^{6} + 464 \, A b c^{7}\right )} e\right )} x^{5} + 128 \, {\left (16 \, {\left (37 \, B b^{2} c^{6} + 70 \, A b c^{7}\right )} d + {\left (3 \, B b^{3} c^{5} + 592 \, A b^{2} c^{6}\right )} e\right )} x^{4} + 48 \, {\left (16 \, {\left (B b^{3} c^{5} + 126 \, A b^{2} c^{6}\right )} d - {\left (9 \, B b^{4} c^{4} - 16 \, A b^{3} c^{5}\right )} e\right )} x^{3} - 56 \, {\left (16 \, {\left (B b^{4} c^{4} - 2 \, A b^{3} c^{5}\right )} d - {\left (9 \, B b^{5} c^{3} - 16 \, A b^{4} c^{4}\right )} e\right )} x^{2} - 1680 \, {\left (B b^{6} c^{2} - 2 \, A b^{5} c^{3}\right )} d + 105 \, {\left (9 \, B b^{7} c - 16 \, A b^{6} c^{2}\right )} e + 70 \, {\left (16 \, {\left (B b^{5} c^{3} - 2 \, A b^{4} c^{4}\right )} d - {\left (9 \, B b^{6} c^{2} - 16 \, A b^{5} c^{3}\right )} e\right )} x\right )} \sqrt {c x^{2} + b x}}{344064 \, c^{6}}\right ] \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 425, normalized size = 1.61 \begin {gather*} \frac {1}{344064} \, \sqrt {c x^{2} + b x} {\left (2 \, {\left (4 \, {\left (2 \, {\left (8 \, {\left (2 \, {\left (12 \, {\left (14 \, B c^{2} x e + \frac {16 \, B c^{9} d + 33 \, B b c^{8} e + 16 \, A c^{9} e}{c^{7}}\right )} x + \frac {464 \, B b c^{8} d + 224 \, A c^{9} d + 243 \, B b^{2} c^{7} e + 464 \, A b c^{8} e}{c^{7}}\right )} x + \frac {592 \, B b^{2} c^{7} d + 1120 \, A b c^{8} d + 3 \, B b^{3} c^{6} e + 592 \, A b^{2} c^{7} e}{c^{7}}\right )} x + \frac {3 \, {\left (16 \, B b^{3} c^{6} d + 2016 \, A b^{2} c^{7} d - 9 \, B b^{4} c^{5} e + 16 \, A b^{3} c^{6} e\right )}}{c^{7}}\right )} x - \frac {7 \, {\left (16 \, B b^{4} c^{5} d - 32 \, A b^{3} c^{6} d - 9 \, B b^{5} c^{4} e + 16 \, A b^{4} c^{5} e\right )}}{c^{7}}\right )} x + \frac {35 \, {\left (16 \, B b^{5} c^{4} d - 32 \, A b^{4} c^{5} d - 9 \, B b^{6} c^{3} e + 16 \, A b^{5} c^{4} e\right )}}{c^{7}}\right )} x - \frac {105 \, {\left (16 \, B b^{6} c^{3} d - 32 \, A b^{5} c^{4} d - 9 \, B b^{7} c^{2} e + 16 \, A b^{6} c^{3} e\right )}}{c^{7}}\right )} - \frac {5 \, {\left (16 \, B b^{7} c d - 32 \, A b^{6} c^{2} d - 9 \, B b^{8} e + 16 \, A b^{7} c e\right )} \log \left ({\left | -2 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x}\right )} \sqrt {c} - b \right |}\right )}{32768 \, c^{\frac {11}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 716, normalized size = 2.71 \begin {gather*} \frac {5 A \,b^{7} e \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x}\right )}{2048 c^{\frac {9}{2}}}-\frac {5 A \,b^{6} d \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x}\right )}{1024 c^{\frac {7}{2}}}-\frac {45 B \,b^{8} e \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x}\right )}{32768 c^{\frac {11}{2}}}+\frac {5 B \,b^{7} d \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x}\right )}{2048 c^{\frac {9}{2}}}-\frac {5 \sqrt {c \,x^{2}+b x}\, A \,b^{5} e x}{512 c^{3}}+\frac {5 \sqrt {c \,x^{2}+b x}\, A \,b^{4} d x}{256 c^{2}}+\frac {45 \sqrt {c \,x^{2}+b x}\, B \,b^{6} e x}{8192 c^{4}}-\frac {5 \sqrt {c \,x^{2}+b x}\, B \,b^{5} d x}{512 c^{3}}-\frac {5 \sqrt {c \,x^{2}+b x}\, A \,b^{6} e}{1024 c^{4}}+\frac {5 \sqrt {c \,x^{2}+b x}\, A \,b^{5} d}{512 c^{3}}+\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} A \,b^{3} e x}{192 c^{2}}-\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} A \,b^{2} d x}{96 c}+\frac {45 \sqrt {c \,x^{2}+b x}\, B \,b^{7} e}{16384 c^{5}}-\frac {5 \sqrt {c \,x^{2}+b x}\, B \,b^{6} d}{1024 c^{4}}-\frac {15 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} B \,b^{4} e x}{1024 c^{3}}+\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} B \,b^{3} d x}{192 c^{2}}+\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} A \,b^{4} e}{384 c^{3}}-\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} A \,b^{3} d}{192 c^{2}}-\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} A b e x}{12 c}+\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} A d x}{6}-\frac {15 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} B \,b^{5} e}{2048 c^{4}}+\frac {5 \left (c \,x^{2}+b x \right )^{\frac {3}{2}} B \,b^{4} d}{384 c^{3}}+\frac {3 \left (c \,x^{2}+b x \right )^{\frac {5}{2}} B \,b^{2} e x}{64 c^{2}}-\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} B b d x}{12 c}-\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} A \,b^{2} e}{24 c^{2}}+\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} A b d}{12 c}+\frac {3 \left (c \,x^{2}+b x \right )^{\frac {5}{2}} B \,b^{3} e}{128 c^{3}}-\frac {\left (c \,x^{2}+b x \right )^{\frac {5}{2}} B \,b^{2} d}{24 c^{2}}+\frac {\left (c \,x^{2}+b x \right )^{\frac {7}{2}} B e x}{8 c}+\frac {\left (c \,x^{2}+b x \right )^{\frac {7}{2}} A e}{7 c}-\frac {9 \left (c \,x^{2}+b x \right )^{\frac {7}{2}} B b e}{112 c^{2}}+\frac {\left (c \,x^{2}+b x \right )^{\frac {7}{2}} B d}{7 c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 573, normalized size = 2.17 \begin {gather*} \frac {1}{6} \, {\left (c x^{2} + b x\right )}^{\frac {5}{2}} A d x + \frac {5 \, \sqrt {c x^{2} + b x} A b^{4} d x}{256 \, c^{2}} - \frac {5 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} A b^{2} d x}{96 \, c} + \frac {45 \, \sqrt {c x^{2} + b x} B b^{6} e x}{8192 \, c^{4}} - \frac {15 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} B b^{4} e x}{1024 \, c^{3}} + \frac {3 \, {\left (c x^{2} + b x\right )}^{\frac {5}{2}} B b^{2} e x}{64 \, c^{2}} + \frac {{\left (c x^{2} + b x\right )}^{\frac {7}{2}} B e x}{8 \, c} - \frac {5 \, A b^{6} d \log \left (2 \, c x + b + 2 \, \sqrt {c x^{2} + b x} \sqrt {c}\right )}{1024 \, c^{\frac {7}{2}}} - \frac {45 \, B b^{8} e \log \left (2 \, c x + b + 2 \, \sqrt {c x^{2} + b x} \sqrt {c}\right )}{32768 \, c^{\frac {11}{2}}} + \frac {5 \, \sqrt {c x^{2} + b x} A b^{5} d}{512 \, c^{3}} - \frac {5 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} A b^{3} d}{192 \, c^{2}} + \frac {{\left (c x^{2} + b x\right )}^{\frac {5}{2}} A b d}{12 \, c} + \frac {45 \, \sqrt {c x^{2} + b x} B b^{7} e}{16384 \, c^{5}} - \frac {15 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} B b^{5} e}{2048 \, c^{4}} + \frac {3 \, {\left (c x^{2} + b x\right )}^{\frac {5}{2}} B b^{3} e}{128 \, c^{3}} - \frac {9 \, {\left (c x^{2} + b x\right )}^{\frac {7}{2}} B b e}{112 \, c^{2}} - \frac {5 \, \sqrt {c x^{2} + b x} {\left (B d + A e\right )} b^{5} x}{512 \, c^{3}} + \frac {5 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} {\left (B d + A e\right )} b^{3} x}{192 \, c^{2}} - \frac {{\left (c x^{2} + b x\right )}^{\frac {5}{2}} {\left (B d + A e\right )} b x}{12 \, c} + \frac {5 \, {\left (B d + A e\right )} b^{7} \log \left (2 \, c x + b + 2 \, \sqrt {c x^{2} + b x} \sqrt {c}\right )}{2048 \, c^{\frac {9}{2}}} - \frac {5 \, \sqrt {c x^{2} + b x} {\left (B d + A e\right )} b^{6}}{1024 \, c^{4}} + \frac {5 \, {\left (c x^{2} + b x\right )}^{\frac {3}{2}} {\left (B d + A e\right )} b^{4}}{384 \, c^{3}} - \frac {{\left (c x^{2} + b x\right )}^{\frac {5}{2}} {\left (B d + A e\right )} b^{2}}{24 \, c^{2}} + \frac {{\left (c x^{2} + b x\right )}^{\frac {7}{2}} {\left (B d + A e\right )}}{7 \, c} \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 {\left (c\,x^2+b\,x\right )}^{5/2}\,\left (A+B\,x\right )\,\left (d+e\,x\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (x \left (b + c x\right )\right )^{\frac {5}{2}} \left (A + B x\right ) \left (d + e x\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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