Optimal. Leaf size=51 \[ -\frac {a^2 A}{6 x^6}-\frac {a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac {1}{3} b^2 B x^3 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 51, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {446, 76} \[ -\frac {a^2 A}{6 x^6}-\frac {a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac {1}{3} b^2 B x^3 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 76
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^7} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^2 (A+B x)}{x^3} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (b^2 B+\frac {a^2 A}{x^3}+\frac {a (2 A b+a B)}{x^2}+\frac {b (A b+2 a B)}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^2 A}{6 x^6}-\frac {a (2 A b+a B)}{3 x^3}+\frac {1}{3} b^2 B x^3+b (A b+2 a B) \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 51, normalized size = 1.00 \[ \frac {1}{6} \left (-\frac {a^2 \left (A+2 B x^3\right )}{x^6}+6 b \log (x) (2 a B+A b)-\frac {4 a A b}{x^3}+2 b^2 B x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.00, size = 55, normalized size = 1.08 \[ \frac {2 \, B b^{2} x^{9} + 6 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} \log \relax (x) - 2 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} - A a^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 70, normalized size = 1.37 \[ \frac {1}{3} \, B b^{2} x^{3} + {\left (2 \, B a b + A b^{2}\right )} \log \left ({\left | x \right |}\right ) - \frac {6 \, B a b x^{6} + 3 \, A b^{2} x^{6} + 2 \, B a^{2} x^{3} + 4 \, A a b x^{3} + A a^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 51, normalized size = 1.00 \[ \frac {B \,b^{2} x^{3}}{3}+A \,b^{2} \ln \relax (x )+2 B a b \ln \relax (x )-\frac {2 A a b}{3 x^{3}}-\frac {B \,a^{2}}{3 x^{3}}-\frac {A \,a^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.67, size = 54, normalized size = 1.06 \[ \frac {1}{3} \, B b^{2} x^{3} + \frac {1}{3} \, {\left (2 \, B a b + A b^{2}\right )} \log \left (x^{3}\right ) - \frac {2 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.36, size = 52, normalized size = 1.02 \[ \ln \relax (x)\,\left (A\,b^2+2\,B\,a\,b\right )-\frac {x^3\,\left (\frac {B\,a^2}{3}+\frac {2\,A\,b\,a}{3}\right )+\frac {A\,a^2}{6}}{x^6}+\frac {B\,b^2\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.76, size = 51, normalized size = 1.00 \[ \frac {B b^{2} x^{3}}{3} + b \left (A b + 2 B a\right ) \log {\relax (x )} + \frac {- A a^{2} + x^{3} \left (- 4 A a b - 2 B a^{2}\right )}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________