Optimal. Leaf size=528 \[ -\frac {\tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (2 c^3 \left (6 a^2 h-3 a b g+b^2 f\right )-30 a^2 b c^2 i+10 a b^3 c i-c^4 (6 b e-4 a f)+b^5 (-i)+12 c^5 d\right )}{c^3 \left (b^2-4 a c\right )^{5/2}}-\frac {x \left (c^3 \left (2 a^2 h+3 a b g+b^2 f\right )-b c^2 \left (5 a^2 i+4 a b h+b^2 g\right )+b^3 c (5 a i+b h)-c^4 (2 a f+b e)+b^5 (-i)+2 c^5 d\right )+b c^2 \left (-3 a^2 h+a c f+c^2 d\right )-2 a c^2 \left (a^2 i-a c g+c^2 e\right )-a b^4 i+a b^3 c h-a b^2 c (c g-4 a i)}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}+\frac {-b^2 c^2 \left (39 a^2 i-5 a c g+3 c^2 e\right )+2 c x \left (c^3 \left (-10 a^2 h-3 a b g+b^2 f\right )-b^3 c (15 a i+b h)-c^4 (3 b e-2 a f)+a b c^2 (25 a i+8 b h)+2 b^5 i+6 c^5 d\right )+2 b c^3 \left (11 a^2 h+a c f+3 c^2 d\right )-16 a^2 c^3 (c g-2 a i)-b^4 c (c g-11 a i)+b^3 c^2 (c f-8 a h)+b^6 (-i)+b^5 c h}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}+\frac {i \log \left (a+b x+c x^2\right )}{2 c^3} \]
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Rubi [A] time = 1.31, antiderivative size = 528, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.132, Rules used = {1660, 634, 618, 206, 628} \[ \frac {2 c x \left (c^3 \left (-10 a^2 h-3 a b g+b^2 f\right )-b^3 c (15 a i+b h)-c^4 (3 b e-2 a f)+a b c^2 (25 a i+8 b h)+2 b^5 i+6 c^5 d\right )-b^2 c^2 \left (39 a^2 i-5 a c g+3 c^2 e\right )+2 b c^3 \left (11 a^2 h+a c f+3 c^2 d\right )-16 a^2 c^3 (c g-2 a i)+b^3 c^2 (c f-8 a h)-b^4 c (c g-11 a i)+b^5 c h+b^6 (-i)}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}-\frac {x \left (c^3 \left (2 a^2 h+3 a b g+b^2 f\right )-b c^2 \left (5 a^2 i+4 a b h+b^2 g\right )+b^3 c (5 a i+b h)-c^4 (2 a f+b e)+b^5 (-i)+2 c^5 d\right )+b c^2 \left (-3 a^2 h+a c f+c^2 d\right )-2 a c^2 \left (a^2 i-a c g+c^2 e\right )-a b^2 c (c g-4 a i)+a b^3 c h-a b^4 i}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {\tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (2 c^3 \left (6 a^2 h-3 a b g+b^2 f\right )-30 a^2 b c^2 i+10 a b^3 c i-c^4 (6 b e-4 a f)+b^5 (-i)+12 c^5 d\right )}{c^3 \left (b^2-4 a c\right )^{5/2}}+\frac {i \log \left (a+b x+c x^2\right )}{2 c^3} \]
Antiderivative was successfully verified.
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Rule 206
Rule 618
Rule 628
Rule 634
Rule 1660
Rubi steps
\begin {align*} \int \frac {d+e x+f x^2+g x^3+h x^4+372 x^5}{\left (a+b x+c x^2\right )^3} \, dx &=\frac {744 a^3 c^2-b c^4 d-a^2 c \left (1488 b^2+2 c^2 g-3 b c h\right )+a \left (372 b^4+2 c^4 e-b c^3 f+b^2 c^2 g-b^3 c h\right )+\left (372 b^5-b^3 c (1860 a-c g)+b c^2 \left (1860 a^2+c^2 e-3 a c g\right )-b^4 c h-b^2 c^2 (c f-4 a h)-2 c^3 \left (c^2 d-a c f+a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {\int \frac {-\frac {372 b^5-b^3 c (1116 a-c g)-b c^2 \left (372 a^2-3 c^2 e+a c g\right )-b^4 c h-b^2 c^2 (c f-2 a h)-2 c^3 \left (3 c^2 d+a c f-a^2 h\right )}{c^4}-\frac {2 \left (b^2-4 a c\right ) \left (372 b^2-c (372 a-c g)-b c h\right ) x}{c^3}+\frac {2 \left (b^2-4 a c\right ) (372 b-c h) x^2}{c^2}+744 \left (4 a-\frac {b^2}{c}\right ) x^3}{\left (a+b x+c x^2\right )^2} \, dx}{2 \left (b^2-4 a c\right )}\\ &=\frac {744 a^3 c^2-b c^4 d-a^2 c \left (1488 b^2+2 c^2 g-3 b c h\right )+a \left (372 b^4+2 c^4 e-b c^3 f+b^2 c^2 g-b^3 c h\right )+\left (372 b^5-b^3 c (1860 a-c g)+b c^2 \left (1860 a^2+c^2 e-3 a c g\right )-b^4 c h-b^2 c^2 (c f-4 a h)-2 c^3 \left (c^2 d-a c f+a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {372 b^6-16 a^2 c^3 (744 a-c g)-b^4 c (4092 a-c g)+b^2 c^2 \left (14508 a^2+3 c^2 e-5 a c g\right )-b^5 c h-b^3 c^2 (c f-8 a h)-2 b c^3 \left (3 c^2 d+a c f+11 a^2 h\right )-2 c \left (744 b^5-5580 a b^3 c+3 b c^2 \left (3100 a^2-c^2 e-a c g\right )-b^4 c h+b^2 c^2 (c f+8 a h)+2 c^3 \left (3 c^2 d+a c f-5 a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}+\frac {\int \frac {2 \left (6 c^2 d-3 b c e+b^2 f+a \left (\frac {372 b^3}{c^2}+2 c f-3 b g\right )-6 a^2 \left (\frac {434 b}{c}-h\right )\right )+\frac {744 \left (b^2-4 a c\right )^2 x}{c^2}}{a+b x+c x^2} \, dx}{2 \left (b^2-4 a c\right )^2}\\ &=\frac {744 a^3 c^2-b c^4 d-a^2 c \left (1488 b^2+2 c^2 g-3 b c h\right )+a \left (372 b^4+2 c^4 e-b c^3 f+b^2 c^2 g-b^3 c h\right )+\left (372 b^5-b^3 c (1860 a-c g)+b c^2 \left (1860 a^2+c^2 e-3 a c g\right )-b^4 c h-b^2 c^2 (c f-4 a h)-2 c^3 \left (c^2 d-a c f+a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {372 b^6-16 a^2 c^3 (744 a-c g)-b^4 c (4092 a-c g)+b^2 c^2 \left (14508 a^2+3 c^2 e-5 a c g\right )-b^5 c h-b^3 c^2 (c f-8 a h)-2 b c^3 \left (3 c^2 d+a c f+11 a^2 h\right )-2 c \left (744 b^5-5580 a b^3 c+3 b c^2 \left (3100 a^2-c^2 e-a c g\right )-b^4 c h+b^2 c^2 (c f+8 a h)+2 c^3 \left (3 c^2 d+a c f-5 a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}+\frac {186 \int \frac {b+2 c x}{a+b x+c x^2} \, dx}{c^3}-\frac {\left (186 b^5-1860 a b^3 c-b^2 c^3 f+3 b c^2 \left (1860 a^2+c^2 e+a c g\right )-2 c^3 \left (3 c^2 d+a c f+3 a^2 h\right )\right ) \int \frac {1}{a+b x+c x^2} \, dx}{c^3 \left (b^2-4 a c\right )^2}\\ &=\frac {744 a^3 c^2-b c^4 d-a^2 c \left (1488 b^2+2 c^2 g-3 b c h\right )+a \left (372 b^4+2 c^4 e-b c^3 f+b^2 c^2 g-b^3 c h\right )+\left (372 b^5-b^3 c (1860 a-c g)+b c^2 \left (1860 a^2+c^2 e-3 a c g\right )-b^4 c h-b^2 c^2 (c f-4 a h)-2 c^3 \left (c^2 d-a c f+a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {372 b^6-16 a^2 c^3 (744 a-c g)-b^4 c (4092 a-c g)+b^2 c^2 \left (14508 a^2+3 c^2 e-5 a c g\right )-b^5 c h-b^3 c^2 (c f-8 a h)-2 b c^3 \left (3 c^2 d+a c f+11 a^2 h\right )-2 c \left (744 b^5-5580 a b^3 c+3 b c^2 \left (3100 a^2-c^2 e-a c g\right )-b^4 c h+b^2 c^2 (c f+8 a h)+2 c^3 \left (3 c^2 d+a c f-5 a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}+\frac {186 \log \left (a+b x+c x^2\right )}{c^3}+\frac {\left (2 \left (186 b^5-1860 a b^3 c-b^2 c^3 f+3 b c^2 \left (1860 a^2+c^2 e+a c g\right )-2 c^3 \left (3 c^2 d+a c f+3 a^2 h\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{b^2-4 a c-x^2} \, dx,x,b+2 c x\right )}{c^3 \left (b^2-4 a c\right )^2}\\ &=\frac {744 a^3 c^2-b c^4 d-a^2 c \left (1488 b^2+2 c^2 g-3 b c h\right )+a \left (372 b^4+2 c^4 e-b c^3 f+b^2 c^2 g-b^3 c h\right )+\left (372 b^5-b^3 c (1860 a-c g)+b c^2 \left (1860 a^2+c^2 e-3 a c g\right )-b^4 c h-b^2 c^2 (c f-4 a h)-2 c^3 \left (c^2 d-a c f+a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2}-\frac {372 b^6-16 a^2 c^3 (744 a-c g)-b^4 c (4092 a-c g)+b^2 c^2 \left (14508 a^2+3 c^2 e-5 a c g\right )-b^5 c h-b^3 c^2 (c f-8 a h)-2 b c^3 \left (3 c^2 d+a c f+11 a^2 h\right )-2 c \left (744 b^5-5580 a b^3 c+3 b c^2 \left (3100 a^2-c^2 e-a c g\right )-b^4 c h+b^2 c^2 (c f+8 a h)+2 c^3 \left (3 c^2 d+a c f-5 a^2 h\right )\right ) x}{2 c^4 \left (b^2-4 a c\right )^2 \left (a+b x+c x^2\right )}+\frac {2 \left (186 b^5-1860 a b^3 c-b^2 c^3 f+3 b c^2 \left (1860 a^2+c^2 e+a c g\right )-2 c^3 \left (3 c^2 d+a c f+3 a^2 h\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{c^3 \left (b^2-4 a c\right )^{5/2}}+\frac {186 \log \left (a+b x+c x^2\right )}{c^3}\\ \end {align*}
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Mathematica [A] time = 1.08, size = 488, normalized size = 0.92 \[ \frac {\frac {2 c \tan ^{-1}\left (\frac {b+2 c x}{\sqrt {4 a c-b^2}}\right ) \left (2 c^3 \left (6 a^2 h-3 a b g+b^2 f\right )-30 a^2 b c^2 i+10 a b^3 c i+c^4 (4 a f-6 b e)+b^5 (-i)+12 c^5 d\right )}{\left (4 a c-b^2\right )^{5/2}}+\frac {b^2 c \left (-4 a^2 i+a c (g+4 h x)-c^2 f x\right )+b c^2 \left (a^2 (3 h+5 i x)-a c (f+3 g x)+c^2 (e x-d)\right )+2 c^2 \left (a^3 i-a^2 c (g+h x)+a c^2 (e+f x)-c^3 d x\right )+b^4 (a i-c h x)+b^3 c (c g x-a (h+5 i x))+b^5 i x}{\left (b^2-4 a c\right ) (a+x (b+c x))^2}+\frac {b^2 c^2 \left (-39 a^2 i+a c (5 g+16 h x)+c^2 (2 f x-3 e)\right )+2 b c^3 \left (a^2 (11 h+25 i x)+a c (f-3 g x)+3 c^2 (d-e x)\right )+4 c^3 \left (8 a^3 i-a^2 c (4 g+5 h x)+a c^2 f x+3 c^3 d x\right )-b^4 c (c (g+2 h x)-11 a i)+b^3 c^2 (-8 a h-30 a i x+c f)+b^6 (-i)+b^5 c (h+4 i x)}{\left (b^2-4 a c\right )^2 (a+x (b+c x))}+c i \log (a+x (b+c x))}{2 c^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.99, size = 3480, normalized size = 6.59 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 657, normalized size = 1.24 \[ \frac {{\left (12 \, c^{5} d i + 2 \, b^{2} c^{3} f i + 4 \, a c^{4} f i - 6 \, a b c^{3} g i + 12 \, a^{2} c^{3} h i - 6 \, b c^{4} i e + b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right )} \arctan \left (\frac {2 \, c x + b}{\sqrt {-b^{2} + 4 \, a c}}\right )}{{\left (b^{4} c^{3} i - 8 \, a b^{2} c^{4} i + 16 \, a^{2} c^{5} i\right )} \sqrt {-b^{2} + 4 \, a c}} + \frac {i \log \left (c x^{2} + b x + a\right )}{2 \, c^{3}} - \frac {b^{3} c^{3} d - 10 \, a b c^{4} d - 6 \, a^{2} b c^{3} f + a^{2} b^{2} c^{2} g + 8 \, a^{3} c^{3} g + a^{2} b^{3} c h - 10 \, a^{3} b c^{2} h - 3 \, a^{2} b^{4} i + 21 \, a^{3} b^{2} c i - 24 \, a^{4} c^{2} i + a b^{2} c^{3} e + 8 \, a^{2} c^{4} e - 2 \, {\left (6 \, c^{6} d + b^{2} c^{4} f + 2 \, a c^{5} f - 3 \, a b c^{4} g - b^{4} c^{2} h + 8 \, a b^{2} c^{3} h - 10 \, a^{2} c^{4} h + 2 \, b^{5} c i - 15 \, a b^{3} c^{2} i + 25 \, a^{2} b c^{3} i - 3 \, b c^{5} e\right )} x^{3} - {\left (18 \, b c^{5} d + 3 \, b^{3} c^{3} f + 6 \, a b c^{4} f - b^{4} c^{2} g - a b^{2} c^{3} g - 16 \, a^{2} c^{4} g - b^{5} c h + 8 \, a b^{3} c^{2} h + 2 \, a^{2} b c^{3} h + 3 \, b^{6} i - 19 \, a b^{4} c i + 11 \, a^{2} b^{2} c^{2} i + 32 \, a^{3} c^{3} i - 9 \, b^{2} c^{4} e\right )} x^{2} - 2 \, {\left (2 \, b^{2} c^{4} d + 10 \, a c^{5} d + 5 \, a b^{2} c^{3} f - 2 \, a^{2} c^{4} f - a b^{3} c^{2} g - 5 \, a^{2} b c^{3} g - a b^{4} c h + 10 \, a^{2} b^{2} c^{2} h - 6 \, a^{3} c^{3} h + 3 \, a b^{5} i - 22 \, a^{2} b^{3} c i + 31 \, a^{3} b c^{2} i - b^{3} c^{3} e - 5 \, a b c^{4} e\right )} x}{2 \, {\left (c x^{2} + b x + a\right )}^{2} {\left (b^{2} - 4 \, a c\right )}^{2} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 1244, normalized size = 2.36 \[ -\frac {30 a^{2} b i \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}\, c}+\frac {12 a^{2} h \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}+\frac {10 a \,b^{3} i \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}\, c^{2}}-\frac {6 a b g \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}+\frac {4 a c f \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}-\frac {b^{5} i \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}\, c^{3}}+\frac {2 b^{2} f \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}-\frac {6 b c e \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}+\frac {12 c^{2} d \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) \sqrt {4 a c -b^{2}}}+\frac {8 a^{2} i \ln \left (c \,x^{2}+b x +a \right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c}-\frac {4 a \,b^{2} i \ln \left (c \,x^{2}+b x +a \right )}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{2}}+\frac {b^{4} i \ln \left (c \,x^{2}+b x +a \right )}{2 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{3}}+\frac {\frac {\left (25 a^{2} b \,c^{2} i -10 a^{2} c^{3} h -15 a \,b^{3} c i +8 a \,b^{2} c^{2} h -3 a b \,c^{3} g +2 a \,c^{4} f +2 b^{5} i -b^{4} c h +b^{2} c^{3} f -3 b \,c^{4} e +6 c^{5} d \right ) x^{3}}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{2}}+\frac {\left (32 a^{3} c^{3} i +11 a^{2} b^{2} c^{2} i +2 a^{2} b \,c^{3} h -16 a^{2} c^{4} g -19 a \,b^{4} c i +8 a \,b^{3} c^{2} h -a \,b^{2} c^{3} g +6 a b \,c^{4} f +3 b^{6} i -b^{5} c h -b^{4} c^{2} g +3 b^{3} c^{3} f -9 b^{2} c^{4} e +18 b \,c^{5} d \right ) x^{2}}{2 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{3}}+\frac {\left (31 a^{3} b \,c^{2} i -6 a^{3} c^{3} h -22 a^{2} b^{3} c i +10 a^{2} b^{2} c^{2} h -5 a^{2} b \,c^{3} g -2 a^{2} c^{4} f +3 a \,b^{5} i -a \,b^{4} c h -a \,b^{3} c^{2} g +5 a \,b^{2} c^{3} f -5 a b \,c^{4} e +10 a \,c^{5} d -b^{3} c^{3} e +2 b^{2} c^{4} d \right ) x}{\left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{3}}+\frac {24 a^{4} c^{2} i -21 a^{3} b^{2} c i +10 a^{3} b \,c^{2} h -8 a^{3} c^{3} g +3 a^{2} b^{4} i -a^{2} b^{3} c h -a^{2} b^{2} c^{2} g +6 a^{2} b \,c^{3} f -8 a^{2} c^{4} e -a \,b^{2} c^{3} e +10 a b \,c^{4} d -b^{3} c^{3} d}{2 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) c^{3}}}{\left (c \,x^{2}+b x +a \right )^{2}} \]
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 \[ \text {Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.17, size = 1027, normalized size = 1.95 \[ \frac {\mathrm {atan}\left (\frac {x\,\left (32\,a^2\,c^5\,{\left (4\,a\,c-b^2\right )}^{5/2}+2\,b^4\,c^3\,{\left (4\,a\,c-b^2\right )}^{5/2}-16\,a\,b^2\,c^4\,{\left (4\,a\,c-b^2\right )}^{5/2}\right )}{c^2\,{\left (4\,a\,c-b^2\right )}^5}+\frac {\left (32\,a^2\,c^5\,{\left (4\,a\,c-b^2\right )}^{5/2}+2\,b^4\,c^3\,{\left (4\,a\,c-b^2\right )}^{5/2}-16\,a\,b^2\,c^4\,{\left (4\,a\,c-b^2\right )}^{5/2}\right )\,\left (16\,a^2\,b\,c^4-8\,a\,b^3\,c^3+b^5\,c^2\right )}{2\,c^5\,{\left (4\,a\,c-b^2\right )}^5\,\left (16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right )}\right )\,\left (-30\,i\,a^2\,b\,c^2+12\,h\,a^2\,c^3+10\,i\,a\,b^3\,c-6\,g\,a\,b\,c^3+4\,f\,a\,c^4-i\,b^5+2\,f\,b^2\,c^3-6\,e\,b\,c^4+12\,d\,c^5\right )}{c^3\,{\left (4\,a\,c-b^2\right )}^{5/2}}-\frac {\ln \left (c\,x^2+b\,x+a\right )\,\left (-1024\,i\,a^5\,c^5+1280\,i\,a^4\,b^2\,c^4-640\,i\,a^3\,b^4\,c^3+160\,i\,a^2\,b^6\,c^2-20\,i\,a\,b^8\,c+i\,b^{10}\right )}{2\,\left (1024\,a^5\,c^8-1280\,a^4\,b^2\,c^7+640\,a^3\,b^4\,c^6-160\,a^2\,b^6\,c^5+20\,a\,b^8\,c^4-b^{10}\,c^3\right )}-\frac {\frac {-24\,i\,a^4\,c^2+21\,i\,a^3\,b^2\,c-10\,h\,a^3\,b\,c^2+8\,g\,a^3\,c^3-3\,i\,a^2\,b^4+h\,a^2\,b^3\,c+g\,a^2\,b^2\,c^2-6\,f\,a^2\,b\,c^3+8\,e\,a^2\,c^4+e\,a\,b^2\,c^3-10\,d\,a\,b\,c^4+d\,b^3\,c^3}{2\,c^3\,\left (16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right )}-\frac {x^2\,\left (32\,i\,a^3\,c^3+11\,i\,a^2\,b^2\,c^2+2\,h\,a^2\,b\,c^3-16\,g\,a^2\,c^4-19\,i\,a\,b^4\,c+8\,h\,a\,b^3\,c^2-g\,a\,b^2\,c^3+6\,f\,a\,b\,c^4+3\,i\,b^6-h\,b^5\,c-g\,b^4\,c^2+3\,f\,b^3\,c^3-9\,e\,b^2\,c^4+18\,d\,b\,c^5\right )}{2\,c^3\,\left (16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right )}+\frac {x\,\left (-31\,i\,a^3\,b\,c^2+6\,h\,a^3\,c^3+22\,i\,a^2\,b^3\,c-10\,h\,a^2\,b^2\,c^2+5\,g\,a^2\,b\,c^3+2\,f\,a^2\,c^4-3\,i\,a\,b^5+h\,a\,b^4\,c+g\,a\,b^3\,c^2-5\,f\,a\,b^2\,c^3+5\,e\,a\,b\,c^4-10\,d\,a\,c^5+e\,b^3\,c^3-2\,d\,b^2\,c^4\right )}{c^3\,\left (16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right )}-\frac {x^3\,\left (25\,i\,a^2\,b\,c^2-10\,h\,a^2\,c^3-15\,i\,a\,b^3\,c+8\,h\,a\,b^2\,c^2-3\,g\,a\,b\,c^3+2\,f\,a\,c^4+2\,i\,b^5-h\,b^4\,c+f\,b^2\,c^3-3\,e\,b\,c^4+6\,d\,c^5\right )}{c^2\,\left (16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right )}}{x^2\,\left (b^2+2\,a\,c\right )+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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