Optimal. Leaf size=72 \[ -\frac {b (a+b x)^7 (2 A b-9 a B)}{504 a^3 x^7}+\frac {(a+b x)^7 (2 A b-9 a B)}{72 a^2 x^8}-\frac {A (a+b x)^7}{9 a x^9} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {27, 78, 45, 37} \begin {gather*} -\frac {b (a+b x)^7 (2 A b-9 a B)}{504 a^3 x^7}+\frac {(a+b x)^7 (2 A b-9 a B)}{72 a^2 x^8}-\frac {A (a+b x)^7}{9 a x^9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 37
Rule 45
Rule 78
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^3}{x^{10}} \, dx &=\int \frac {(a+b x)^6 (A+B x)}{x^{10}} \, dx\\ &=-\frac {A (a+b x)^7}{9 a x^9}+\frac {(-2 A b+9 a B) \int \frac {(a+b x)^6}{x^9} \, dx}{9 a}\\ &=-\frac {A (a+b x)^7}{9 a x^9}+\frac {(2 A b-9 a B) (a+b x)^7}{72 a^2 x^8}+\frac {(b (2 A b-9 a B)) \int \frac {(a+b x)^6}{x^8} \, dx}{72 a^2}\\ &=-\frac {A (a+b x)^7}{9 a x^9}+\frac {(2 A b-9 a B) (a+b x)^7}{72 a^2 x^8}-\frac {b (2 A b-9 a B) (a+b x)^7}{504 a^3 x^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 126, normalized size = 1.75 \begin {gather*} -\frac {7 a^6 (8 A+9 B x)+54 a^5 b x (7 A+8 B x)+180 a^4 b^2 x^2 (6 A+7 B x)+336 a^3 b^3 x^3 (5 A+6 B x)+378 a^2 b^4 x^4 (4 A+5 B x)+252 a b^5 x^5 (3 A+4 B x)+84 b^6 x^6 (2 A+3 B x)}{504 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 )^3}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.39, size = 147, normalized size = 2.04 \begin {gather*} -\frac {252 \, B b^{6} x^{7} + 56 \, A a^{6} + 168 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 378 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 504 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 420 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 216 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 63 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x}{504 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.18, size = 147, normalized size = 2.04 \begin {gather*} -\frac {252 \, B b^{6} x^{7} + 1008 \, B a b^{5} x^{6} + 168 \, A b^{6} x^{6} + 1890 \, B a^{2} b^{4} x^{5} + 756 \, A a b^{5} x^{5} + 2016 \, B a^{3} b^{3} x^{4} + 1512 \, A a^{2} b^{4} x^{4} + 1260 \, B a^{4} b^{2} x^{3} + 1680 \, A a^{3} b^{3} x^{3} + 432 \, B a^{5} b x^{2} + 1080 \, A a^{4} b^{2} x^{2} + 63 \, B a^{6} x + 378 \, A a^{5} b x + 56 \, A a^{6}}{504 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 128, normalized size = 1.78 \begin {gather*} -\frac {B \,b^{6}}{2 x^{2}}-\frac {\left (A b +6 B a \right ) b^{5}}{3 x^{3}}-\frac {3 \left (2 A b +5 B a \right ) a \,b^{4}}{4 x^{4}}-\frac {\left (3 A b +4 B a \right ) a^{2} b^{3}}{x^{5}}-\frac {5 \left (4 A b +3 B a \right ) a^{3} b^{2}}{6 x^{6}}-\frac {A \,a^{6}}{9 x^{9}}-\frac {3 \left (5 A b +2 B a \right ) a^{4} b}{7 x^{7}}-\frac {\left (6 A b +B a \right ) a^{5}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.56, size = 147, normalized size = 2.04 \begin {gather*} -\frac {252 \, B b^{6} x^{7} + 56 \, A a^{6} + 168 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 378 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 504 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 420 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 216 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 63 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x}{504 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.07, size = 143, normalized size = 1.99 \begin {gather*} -\frac {x\,\left (\frac {B\,a^6}{8}+\frac {3\,A\,b\,a^5}{4}\right )+\frac {A\,a^6}{9}+x^5\,\left (\frac {15\,B\,a^2\,b^4}{4}+\frac {3\,A\,a\,b^5}{2}\right )+x^2\,\left (\frac {6\,B\,a^5\,b}{7}+\frac {15\,A\,a^4\,b^2}{7}\right )+x^6\,\left (\frac {A\,b^6}{3}+2\,B\,a\,b^5\right )+x^4\,\left (4\,B\,a^3\,b^3+3\,A\,a^2\,b^4\right )+x^3\,\left (\frac {5\,B\,a^4\,b^2}{2}+\frac {10\,A\,a^3\,b^3}{3}\right )+\frac {B\,b^6\,x^7}{2}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 6.88, size = 158, normalized size = 2.19 \begin {gather*} \frac {- 56 A a^{6} - 252 B b^{6} x^{7} + x^{6} \left (- 168 A b^{6} - 1008 B a b^{5}\right ) + x^{5} \left (- 756 A a b^{5} - 1890 B a^{2} b^{4}\right ) + x^{4} \left (- 1512 A a^{2} b^{4} - 2016 B a^{3} b^{3}\right ) + x^{3} \left (- 1680 A a^{3} b^{3} - 1260 B a^{4} b^{2}\right ) + x^{2} \left (- 1080 A a^{4} b^{2} - 432 B a^{5} b\right ) + x \left (- 378 A a^{5} b - 63 B a^{6}\right )}{504 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________