Optimal. Leaf size=53 \[ -\frac {2 (a B+A b)}{5 x^{5/2}}-\frac {2 a A}{7 x^{7/2}}-\frac {2 (A c+b B)}{3 x^{3/2}}-\frac {2 B c}{\sqrt {x}} \]
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Rubi [A] time = 0.03, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {765} \[ -\frac {2 (a B+A b)}{5 x^{5/2}}-\frac {2 a A}{7 x^{7/2}}-\frac {2 (A c+b B)}{3 x^{3/2}}-\frac {2 B c}{\sqrt {x}} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a+b x+c x^2\right )}{x^{9/2}} \, dx &=\int \left (\frac {a A}{x^{9/2}}+\frac {A b+a B}{x^{7/2}}+\frac {b B+A c}{x^{5/2}}+\frac {B c}{x^{3/2}}\right ) \, dx\\ &=-\frac {2 a A}{7 x^{7/2}}-\frac {2 (A b+a B)}{5 x^{5/2}}-\frac {2 (b B+A c)}{3 x^{3/2}}-\frac {2 B c}{\sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 45, normalized size = 0.85 \[ -\frac {2 (3 a (5 A+7 B x)+7 x (A (3 b+5 c x)+5 B x (b+3 c x)))}{105 x^{7/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 39, normalized size = 0.74 \[ -\frac {2 \, {\left (105 \, B c x^{3} + 35 \, {\left (B b + A c\right )} x^{2} + 15 \, A a + 21 \, {\left (B a + A b\right )} x\right )}}{105 \, x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 41, normalized size = 0.77 \[ -\frac {2 \, {\left (105 \, B c x^{3} + 35 \, B b x^{2} + 35 \, A c x^{2} + 21 \, B a x + 21 \, A b x + 15 \, A a\right )}}{105 \, x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 42, normalized size = 0.79 \[ -\frac {2 \left (105 B c \,x^{3}+35 A c \,x^{2}+35 B b \,x^{2}+21 A b x +21 B a x +15 A a \right )}{105 x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 39, normalized size = 0.74 \[ -\frac {2 \, {\left (105 \, B c x^{3} + 35 \, {\left (B b + A c\right )} x^{2} + 15 \, A a + 21 \, {\left (B a + A b\right )} x\right )}}{105 \, x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.77 \[ -\frac {2\,B\,c\,x^3+\left (\frac {2\,A\,c}{3}+\frac {2\,B\,b}{3}\right )\,x^2+\left (\frac {2\,A\,b}{5}+\frac {2\,B\,a}{5}\right )\,x+\frac {2\,A\,a}{7}}{x^{7/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.09, size = 70, normalized size = 1.32 \[ - \frac {2 A a}{7 x^{\frac {7}{2}}} - \frac {2 A b}{5 x^{\frac {5}{2}}} - \frac {2 A c}{3 x^{\frac {3}{2}}} - \frac {2 B a}{5 x^{\frac {5}{2}}} - \frac {2 B b}{3 x^{\frac {3}{2}}} - \frac {2 B c}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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