Optimal. Leaf size=312 \[ -\frac {e \left (b^2-4 a c\right )^2 \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{512 c^{9/2}}+\frac {e \left (b^2-4 a c\right ) (b+2 c x) \sqrt {a+b x+c x^2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right )}{256 c^4}+\frac {\left (a+b x+c x^2\right )^{3/2} \left (6 c e x \left (-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right )-24 c^2 d e (16 a e+3 b d)+12 b c e^2 (11 a e+10 b d)-35 b^3 e^3+64 c^3 d^3\right )}{480 c^3}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {(d+e x)^2 \left (a+b x+c x^2\right )^{3/2} (2 c d-b e)}{10 c} \]
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Rubi [A] time = 0.42, antiderivative size = 312, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {832, 779, 612, 621, 206} \begin {gather*} \frac {\left (a+b x+c x^2\right )^{3/2} \left (6 c e x \left (-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right )-24 c^2 d e (16 a e+3 b d)+12 b c e^2 (11 a e+10 b d)-35 b^3 e^3+64 c^3 d^3\right )}{480 c^3}+\frac {e \left (b^2-4 a c\right ) (b+2 c x) \sqrt {a+b x+c x^2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right )}{256 c^4}-\frac {e \left (b^2-4 a c\right )^2 \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{512 c^{9/2}}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {(d+e x)^2 \left (a+b x+c x^2\right )^{3/2} (2 c d-b e)}{10 c} \end {gather*}
Antiderivative was successfully verified.
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Rule 206
Rule 612
Rule 621
Rule 779
Rule 832
Rubi steps
\begin {align*} \int (b+2 c x) (d+e x)^3 \sqrt {a+b x+c x^2} \, dx &=\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\int (d+e x)^2 (3 c (b d-2 a e)+3 c (2 c d-b e) x) \sqrt {a+b x+c x^2} \, dx}{6 c}\\ &=\frac {(2 c d-b e) (d+e x)^2 \left (a+b x+c x^2\right )^{3/2}}{10 c}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\int (d+e x) \left (\frac {3}{2} c \left (3 b^2 d e-28 a c d e+4 b \left (c d^2+a e^2\right )\right )+\frac {3}{2} c \left (8 c^2 d^2+7 b^2 e^2-4 c e (2 b d+5 a e)\right ) x\right ) \sqrt {a+b x+c x^2} \, dx}{30 c^2}\\ &=\frac {(2 c d-b e) (d+e x)^2 \left (a+b x+c x^2\right )^{3/2}}{10 c}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\left (64 c^3 d^3-35 b^3 e^3+12 b c e^2 (10 b d+11 a e)-24 c^2 d e (3 b d+16 a e)+6 c e \left (8 c^2 d^2+7 b^2 e^2-4 c e (2 b d+5 a e)\right ) x\right ) \left (a+b x+c x^2\right )^{3/2}}{480 c^3}+\frac {\left (\left (b^2-4 a c\right ) e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \int \sqrt {a+b x+c x^2} \, dx}{64 c^3}\\ &=\frac {\left (b^2-4 a c\right ) e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b+2 c x) \sqrt {a+b x+c x^2}}{256 c^4}+\frac {(2 c d-b e) (d+e x)^2 \left (a+b x+c x^2\right )^{3/2}}{10 c}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\left (64 c^3 d^3-35 b^3 e^3+12 b c e^2 (10 b d+11 a e)-24 c^2 d e (3 b d+16 a e)+6 c e \left (8 c^2 d^2+7 b^2 e^2-4 c e (2 b d+5 a e)\right ) x\right ) \left (a+b x+c x^2\right )^{3/2}}{480 c^3}-\frac {\left (\left (b^2-4 a c\right )^2 e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \int \frac {1}{\sqrt {a+b x+c x^2}} \, dx}{512 c^4}\\ &=\frac {\left (b^2-4 a c\right ) e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b+2 c x) \sqrt {a+b x+c x^2}}{256 c^4}+\frac {(2 c d-b e) (d+e x)^2 \left (a+b x+c x^2\right )^{3/2}}{10 c}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\left (64 c^3 d^3-35 b^3 e^3+12 b c e^2 (10 b d+11 a e)-24 c^2 d e (3 b d+16 a e)+6 c e \left (8 c^2 d^2+7 b^2 e^2-4 c e (2 b d+5 a e)\right ) x\right ) \left (a+b x+c x^2\right )^{3/2}}{480 c^3}-\frac {\left (\left (b^2-4 a c\right )^2 e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \operatorname {Subst}\left (\int \frac {1}{4 c-x^2} \, dx,x,\frac {b+2 c x}{\sqrt {a+b x+c x^2}}\right )}{256 c^4}\\ &=\frac {\left (b^2-4 a c\right ) e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b+2 c x) \sqrt {a+b x+c x^2}}{256 c^4}+\frac {(2 c d-b e) (d+e x)^2 \left (a+b x+c x^2\right )^{3/2}}{10 c}+\frac {1}{3} (d+e x)^3 \left (a+b x+c x^2\right )^{3/2}+\frac {\left (64 c^3 d^3-35 b^3 e^3+12 b c e^2 (10 b d+11 a e)-24 c^2 d e (3 b d+16 a e)+6 c e \left (8 c^2 d^2+7 b^2 e^2-4 c e (2 b d+5 a e)\right ) x\right ) \left (a+b x+c x^2\right )^{3/2}}{480 c^3}-\frac {\left (b^2-4 a c\right )^2 e \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{512 c^{9/2}}\\ \end {align*}
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Mathematica [A] time = 0.51, size = 270, normalized size = 0.87 \begin {gather*} \frac {1}{6} \left (\frac {(a+x (b+c x))^{3/2} \left (-24 c^2 e (a e (16 d+5 e x)+b d (3 d+2 e x))+6 b c e^2 (22 a e+20 b d+7 b e x)-35 b^3 e^3+16 c^3 d^2 (4 d+3 e x)\right )}{80 c^3}-\frac {3 e \left (b^2-4 a c\right ) \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) \left (\left (b^2-4 a c\right ) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+x (b+c x)}}\right )-2 \sqrt {c} (b+2 c x) \sqrt {a+x (b+c x)}\right )}{256 c^{9/2}}+2 (d+e x)^3 (a+x (b+c x))^{3/2}+\frac {3 (d+e x)^2 (a+x (b+c x))^{3/2} (2 c d-b e)}{5 c}\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 2.01, size = 533, normalized size = 1.71 \begin {gather*} \frac {\sqrt {a+b x+c x^2} \left (1296 a^2 b c^2 e^3-3072 a^2 c^3 d e^2-480 a^2 c^3 e^3 x-760 a b^3 c e^3+2400 a b^2 c^2 d e^2+432 a b^2 c^2 e^3 x-2400 a b c^3 d^2 e-1344 a b c^3 d e^2 x-288 a b c^3 e^3 x^2+2560 a c^4 d^3+2880 a c^4 d^2 e x+1536 a c^4 d e^2 x^2+320 a c^4 e^3 x^3+105 b^5 e^3-360 b^4 c d e^2-70 b^4 c e^3 x+360 b^3 c^2 d^2 e+240 b^3 c^2 d e^2 x+56 b^3 c^2 e^3 x^2-240 b^2 c^3 d^2 e x-192 b^2 c^3 d e^2 x^2-48 b^2 c^3 e^3 x^3+2560 b c^4 d^3 x+4800 b c^4 d^2 e x^2+3456 b c^4 d e^2 x^3+896 b c^4 e^3 x^4+2560 c^5 d^3 x^2+5760 c^5 d^2 e x^3+4608 c^5 d e^2 x^4+1280 c^5 e^3 x^5\right )}{3840 c^4}+\frac {\left (-64 a^3 c^3 e^3+144 a^2 b^2 c^2 e^3-384 a^2 b c^3 d e^2+384 a^2 c^4 d^2 e-60 a b^4 c e^3+192 a b^3 c^2 d e^2-192 a b^2 c^3 d^2 e+7 b^6 e^3-24 b^5 c d e^2+24 b^4 c^2 d^2 e\right ) \log \left (-2 \sqrt {c} \sqrt {a+b x+c x^2}+b+2 c x\right )}{512 c^{9/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 985, normalized size = 3.16 \begin {gather*} \left [-\frac {15 \, {\left (24 \, {\left (b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right )} d^{2} e - 24 \, {\left (b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right )} d e^{2} + {\left (7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right )} e^{3}\right )} \sqrt {c} \log \left (-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt {c x^{2} + b x + a} {\left (2 \, c x + b\right )} \sqrt {c} - 4 \, a c\right ) - 4 \, {\left (1280 \, c^{6} e^{3} x^{5} + 2560 \, a c^{5} d^{3} + 128 \, {\left (36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}\right )} x^{4} + 120 \, {\left (3 \, b^{3} c^{3} - 20 \, a b c^{4}\right )} d^{2} e - 24 \, {\left (15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right )} d e^{2} + {\left (105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right )} e^{3} + 16 \, {\left (360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - {\left (3 \, b^{2} c^{4} - 20 \, a c^{5}\right )} e^{3}\right )} x^{3} + 8 \, {\left (320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, {\left (b^{2} c^{4} - 8 \, a c^{5}\right )} d e^{2} + {\left (7 \, b^{3} c^{3} - 36 \, a b c^{4}\right )} e^{3}\right )} x^{2} + 2 \, {\left (1280 \, b c^{5} d^{3} - 120 \, {\left (b^{2} c^{4} - 12 \, a c^{5}\right )} d^{2} e + 24 \, {\left (5 \, b^{3} c^{3} - 28 \, a b c^{4}\right )} d e^{2} - {\left (35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right )} e^{3}\right )} x\right )} \sqrt {c x^{2} + b x + a}}{15360 \, c^{5}}, \frac {15 \, {\left (24 \, {\left (b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right )} d^{2} e - 24 \, {\left (b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right )} d e^{2} + {\left (7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right )} e^{3}\right )} \sqrt {-c} \arctan \left (\frac {\sqrt {c x^{2} + b x + a} {\left (2 \, c x + b\right )} \sqrt {-c}}{2 \, {\left (c^{2} x^{2} + b c x + a c\right )}}\right ) + 2 \, {\left (1280 \, c^{6} e^{3} x^{5} + 2560 \, a c^{5} d^{3} + 128 \, {\left (36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}\right )} x^{4} + 120 \, {\left (3 \, b^{3} c^{3} - 20 \, a b c^{4}\right )} d^{2} e - 24 \, {\left (15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right )} d e^{2} + {\left (105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right )} e^{3} + 16 \, {\left (360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - {\left (3 \, b^{2} c^{4} - 20 \, a c^{5}\right )} e^{3}\right )} x^{3} + 8 \, {\left (320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, {\left (b^{2} c^{4} - 8 \, a c^{5}\right )} d e^{2} + {\left (7 \, b^{3} c^{3} - 36 \, a b c^{4}\right )} e^{3}\right )} x^{2} + 2 \, {\left (1280 \, b c^{5} d^{3} - 120 \, {\left (b^{2} c^{4} - 12 \, a c^{5}\right )} d^{2} e + 24 \, {\left (5 \, b^{3} c^{3} - 28 \, a b c^{4}\right )} d e^{2} - {\left (35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right )} e^{3}\right )} x\right )} \sqrt {c x^{2} + b x + a}}{7680 \, c^{5}}\right ] \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 506, normalized size = 1.62 \begin {gather*} \frac {1}{3840} \, \sqrt {c x^{2} + b x + a} {\left (2 \, {\left (4 \, {\left (2 \, {\left (8 \, {\left (10 \, c x e^{3} + \frac {36 \, c^{6} d e^{2} + 7 \, b c^{5} e^{3}}{c^{5}}\right )} x + \frac {360 \, c^{6} d^{2} e + 216 \, b c^{5} d e^{2} - 3 \, b^{2} c^{4} e^{3} + 20 \, a c^{5} e^{3}}{c^{5}}\right )} x + \frac {320 \, c^{6} d^{3} + 600 \, b c^{5} d^{2} e - 24 \, b^{2} c^{4} d e^{2} + 192 \, a c^{5} d e^{2} + 7 \, b^{3} c^{3} e^{3} - 36 \, a b c^{4} e^{3}}{c^{5}}\right )} x + \frac {1280 \, b c^{5} d^{3} - 120 \, b^{2} c^{4} d^{2} e + 1440 \, a c^{5} d^{2} e + 120 \, b^{3} c^{3} d e^{2} - 672 \, a b c^{4} d e^{2} - 35 \, b^{4} c^{2} e^{3} + 216 \, a b^{2} c^{3} e^{3} - 240 \, a^{2} c^{4} e^{3}}{c^{5}}\right )} x + \frac {2560 \, a c^{5} d^{3} + 360 \, b^{3} c^{3} d^{2} e - 2400 \, a b c^{4} d^{2} e - 360 \, b^{4} c^{2} d e^{2} + 2400 \, a b^{2} c^{3} d e^{2} - 3072 \, a^{2} c^{4} d e^{2} + 105 \, b^{5} c e^{3} - 760 \, a b^{3} c^{2} e^{3} + 1296 \, a^{2} b c^{3} e^{3}}{c^{5}}\right )} + \frac {{\left (24 \, b^{4} c^{2} d^{2} e - 192 \, a b^{2} c^{3} d^{2} e + 384 \, a^{2} c^{4} d^{2} e - 24 \, b^{5} c d e^{2} + 192 \, a b^{3} c^{2} d e^{2} - 384 \, a^{2} b c^{3} d e^{2} + 7 \, b^{6} e^{3} - 60 \, a b^{4} c e^{3} + 144 \, a^{2} b^{2} c^{2} e^{3} - 64 \, a^{3} c^{3} e^{3}\right )} \log \left ({\left | -2 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} \sqrt {c} - b \right |}\right )}{512 \, c^{\frac {9}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.09, size = 992, normalized size = 3.18 \begin {gather*} \frac {\left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} e^{3} x^{3}}{3}+\frac {a^{3} e^{3} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{8 c^{\frac {3}{2}}}-\frac {9 a^{2} b^{2} e^{3} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{32 c^{\frac {5}{2}}}+\frac {3 a^{2} b d \,e^{2} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{4 c^{\frac {3}{2}}}-\frac {3 a^{2} d^{2} e \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{4 \sqrt {c}}+\frac {15 a \,b^{4} e^{3} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{128 c^{\frac {7}{2}}}-\frac {3 a \,b^{3} d \,e^{2} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{8 c^{\frac {5}{2}}}+\frac {3 a \,b^{2} d^{2} e \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{8 c^{\frac {3}{2}}}-\frac {7 b^{6} e^{3} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{512 c^{\frac {9}{2}}}+\frac {3 b^{5} d \,e^{2} \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{64 c^{\frac {7}{2}}}-\frac {3 b^{4} d^{2} e \ln \left (\frac {c x +\frac {b}{2}}{\sqrt {c}}+\sqrt {c \,x^{2}+b x +a}\right )}{64 c^{\frac {5}{2}}}+\frac {\sqrt {c \,x^{2}+b x +a}\, a^{2} e^{3} x}{8 c}-\frac {\sqrt {c \,x^{2}+b x +a}\, a \,b^{2} e^{3} x}{4 c^{2}}+\frac {3 \sqrt {c \,x^{2}+b x +a}\, a b d \,e^{2} x}{4 c}-\frac {3 \sqrt {c \,x^{2}+b x +a}\, a \,d^{2} e x}{4}+\frac {7 \sqrt {c \,x^{2}+b x +a}\, b^{4} e^{3} x}{128 c^{3}}-\frac {3 \sqrt {c \,x^{2}+b x +a}\, b^{3} d \,e^{2} x}{16 c^{2}}+\frac {3 \sqrt {c \,x^{2}+b x +a}\, b^{2} d^{2} e x}{16 c}-\frac {\left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b \,e^{3} x^{2}}{10 c}+\frac {6 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} d \,e^{2} x^{2}}{5}+\frac {\sqrt {c \,x^{2}+b x +a}\, a^{2} b \,e^{3}}{16 c^{2}}-\frac {\sqrt {c \,x^{2}+b x +a}\, a \,b^{3} e^{3}}{8 c^{3}}+\frac {3 \sqrt {c \,x^{2}+b x +a}\, a \,b^{2} d \,e^{2}}{8 c^{2}}-\frac {3 \sqrt {c \,x^{2}+b x +a}\, a b \,d^{2} e}{8 c}-\frac {\left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} a \,e^{3} x}{4 c}+\frac {7 \sqrt {c \,x^{2}+b x +a}\, b^{5} e^{3}}{256 c^{4}}-\frac {3 \sqrt {c \,x^{2}+b x +a}\, b^{4} d \,e^{2}}{32 c^{3}}+\frac {3 \sqrt {c \,x^{2}+b x +a}\, b^{3} d^{2} e}{32 c^{2}}+\frac {7 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b^{2} e^{3} x}{80 c^{2}}-\frac {3 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b d \,e^{2} x}{10 c}+\frac {3 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} d^{2} e x}{2}+\frac {11 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} a b \,e^{3}}{40 c^{2}}-\frac {4 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} a d \,e^{2}}{5 c}-\frac {7 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b^{3} e^{3}}{96 c^{3}}+\frac {\left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b^{2} d \,e^{2}}{4 c^{2}}-\frac {\left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} b \,d^{2} e}{4 c}+\frac {2 \left (c \,x^{2}+b x +a \right )^{\frac {3}{2}} d^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.08, size = 1679, normalized size = 5.38
result too large to display
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 (b + 2 c x\right ) \left (d + e x\right )^{3} \sqrt {a + b x + c x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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