Optimal. Leaf size=37 \[ -\frac {2 (A c+b B)}{3 x^{3/2}}-\frac {2 A b}{5 x^{5/2}}-\frac {2 B c}{\sqrt {x}} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {765} \begin {gather*} -\frac {2 (A c+b B)}{3 x^{3/2}}-\frac {2 A b}{5 x^{5/2}}-\frac {2 B c}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 765
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (b x+c x^2\right )}{x^{9/2}} \, dx &=\int \left (\frac {A b}{x^{7/2}}+\frac {b B+A c}{x^{5/2}}+\frac {B c}{x^{3/2}}\right ) \, dx\\ &=-\frac {2 A b}{5 x^{5/2}}-\frac {2 (b B+A c)}{3 x^{3/2}}-\frac {2 B c}{\sqrt {x}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 30, normalized size = 0.81 \begin {gather*} -\frac {2 (A (3 b+5 c x)+5 B x (b+3 c x))}{15 x^{5/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.03, size = 31, normalized size = 0.84 \begin {gather*} -\frac {2 \left (3 A b+5 A c x+5 b B x+15 B c x^2\right )}{15 x^{5/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 27, normalized size = 0.73 \begin {gather*} -\frac {2 \, {\left (15 \, B c x^{2} + 3 \, A b + 5 \, {\left (B b + A c\right )} x\right )}}{15 \, x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 27, normalized size = 0.73 \begin {gather*} -\frac {2 \, {\left (15 \, B c x^{2} + 5 \, B b x + 5 \, A c x + 3 \, A b\right )}}{15 \, x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 28, normalized size = 0.76 \begin {gather*} -\frac {2 \left (15 B c \,x^{2}+5 A c x +5 B b x +3 A b \right )}{15 x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 27, normalized size = 0.73 \begin {gather*} -\frac {2 \, {\left (15 \, B c x^{2} + 3 \, A b + 5 \, {\left (B b + A c\right )} x\right )}}{15 \, x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 28, normalized size = 0.76 \begin {gather*} -\frac {2\,B\,c\,x^2+\left (\frac {2\,A\,c}{3}+\frac {2\,B\,b}{3}\right )\,x+\frac {2\,A\,b}{5}}{x^{5/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 2.93, size = 46, normalized size = 1.24 \begin {gather*} - \frac {2 A b}{5 x^{\frac {5}{2}}} - \frac {2 A c}{3 x^{\frac {3}{2}}} - \frac {2 B b}{3 x^{\frac {3}{2}}} - \frac {2 B c}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________