Optimal. Leaf size=99 \[ -\frac {a^4 A}{9 x^9}-\frac {a^3 (a B+4 A b)}{8 x^8}-\frac {2 a^2 b (2 a B+3 A b)}{7 x^7}-\frac {b^3 (4 a B+A b)}{5 x^5}-\frac {a b^2 (3 a B+2 A b)}{3 x^6}-\frac {b^4 B}{4 x^4} \]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 99, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {27, 76} \begin {gather*} -\frac {a^3 (a B+4 A b)}{8 x^8}-\frac {2 a^2 b (2 a B+3 A b)}{7 x^7}-\frac {a^4 A}{9 x^9}-\frac {a b^2 (3 a B+2 A b)}{3 x^6}-\frac {b^3 (4 a B+A b)}{5 x^5}-\frac {b^4 B}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 76
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^2}{x^{10}} \, dx &=\int \frac {(a+b x)^4 (A+B x)}{x^{10}} \, dx\\ &=\int \left (\frac {a^4 A}{x^{10}}+\frac {a^3 (4 A b+a B)}{x^9}+\frac {2 a^2 b (3 A b+2 a B)}{x^8}+\frac {2 a b^2 (2 A b+3 a B)}{x^7}+\frac {b^3 (A b+4 a B)}{x^6}+\frac {b^4 B}{x^5}\right ) \, dx\\ &=-\frac {a^4 A}{9 x^9}-\frac {a^3 (4 A b+a B)}{8 x^8}-\frac {2 a^2 b (3 A b+2 a B)}{7 x^7}-\frac {a b^2 (2 A b+3 a B)}{3 x^6}-\frac {b^3 (A b+4 a B)}{5 x^5}-\frac {b^4 B}{4 x^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 88, normalized size = 0.89 \begin {gather*} -\frac {35 a^4 (8 A+9 B x)+180 a^3 b x (7 A+8 B x)+360 a^2 b^2 x^2 (6 A+7 B x)+336 a b^3 x^3 (5 A+6 B x)+126 b^4 x^4 (4 A+5 B x)}{2520 x^9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^2}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 280 \, A a^{4} + 504 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 840 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 720 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 315 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 2016 \, B a b^{3} x^{4} + 504 \, A b^{4} x^{4} + 2520 \, B a^{2} b^{2} x^{3} + 1680 \, A a b^{3} x^{3} + 1440 \, B a^{3} b x^{2} + 2160 \, A a^{2} b^{2} x^{2} + 315 \, B a^{4} x + 1260 \, A a^{3} b x + 280 \, A a^{4}}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 88, normalized size = 0.89 \begin {gather*} -\frac {B \,b^{4}}{4 x^{4}}-\frac {\left (A b +4 B a \right ) b^{3}}{5 x^{5}}-\frac {\left (2 A b +3 B a \right ) a \,b^{2}}{3 x^{6}}-\frac {A \,a^{4}}{9 x^{9}}-\frac {2 \left (3 A b +2 B a \right ) a^{2} b}{7 x^{7}}-\frac {\left (4 A b +B a \right ) a^{3}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.47, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 280 \, A a^{4} + 504 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 840 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 720 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 315 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 96, normalized size = 0.97 \begin {gather*} -\frac {x\,\left (\frac {B\,a^4}{8}+\frac {A\,b\,a^3}{2}\right )+\frac {A\,a^4}{9}+x^3\,\left (B\,a^2\,b^2+\frac {2\,A\,a\,b^3}{3}\right )+x^2\,\left (\frac {4\,B\,a^3\,b}{7}+\frac {6\,A\,a^2\,b^2}{7}\right )+x^4\,\left (\frac {A\,b^4}{5}+\frac {4\,B\,a\,b^3}{5}\right )+\frac {B\,b^4\,x^5}{4}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 4.55, size = 107, normalized size = 1.08 \begin {gather*} \frac {- 280 A a^{4} - 630 B b^{4} x^{5} + x^{4} \left (- 504 A b^{4} - 2016 B a b^{3}\right ) + x^{3} \left (- 1680 A a b^{3} - 2520 B a^{2} b^{2}\right ) + x^{2} \left (- 2160 A a^{2} b^{2} - 1440 B a^{3} b\right ) + x \left (- 1260 A a^{3} b - 315 B a^{4}\right )}{2520 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________