Optimal. Leaf size=96 \[ -\frac {a^5 (a+b x)^8}{8 b^6}+\frac {5 a^4 (a+b x)^9}{9 b^6}-\frac {a^3 (a+b x)^{10}}{b^6}+\frac {10 a^2 (a+b x)^{11}}{11 b^6}+\frac {(a+b x)^{13}}{13 b^6}-\frac {5 a (a+b x)^{12}}{12 b^6} \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 96, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} \frac {10 a^2 (a+b x)^{11}}{11 b^6}-\frac {a^3 (a+b x)^{10}}{b^6}+\frac {5 a^4 (a+b x)^9}{9 b^6}-\frac {a^5 (a+b x)^8}{8 b^6}+\frac {(a+b x)^{13}}{13 b^6}-\frac {5 a (a+b x)^{12}}{12 b^6} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int x^5 (a+b x)^7 \, dx &=\int \left (-\frac {a^5 (a+b x)^7}{b^5}+\frac {5 a^4 (a+b x)^8}{b^5}-\frac {10 a^3 (a+b x)^9}{b^5}+\frac {10 a^2 (a+b x)^{10}}{b^5}-\frac {5 a (a+b x)^{11}}{b^5}+\frac {(a+b x)^{12}}{b^5}\right ) \, dx\\ &=-\frac {a^5 (a+b x)^8}{8 b^6}+\frac {5 a^4 (a+b x)^9}{9 b^6}-\frac {a^3 (a+b x)^{10}}{b^6}+\frac {10 a^2 (a+b x)^{11}}{11 b^6}-\frac {5 a (a+b x)^{12}}{12 b^6}+\frac {(a+b x)^{13}}{13 b^6}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 92, normalized size = 0.96 \begin {gather*} \frac {a^7 x^6}{6}+a^6 b x^7+\frac {21}{8} a^5 b^2 x^8+\frac {35}{9} a^4 b^3 x^9+\frac {7}{2} a^3 b^4 x^{10}+\frac {21}{11} a^2 b^5 x^{11}+\frac {7}{12} a b^6 x^{12}+\frac {b^7 x^{13}}{13} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^5 (a+b x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.34, size = 78, normalized size = 0.81 \begin {gather*} \frac {1}{13} x^{13} b^{7} + \frac {7}{12} x^{12} b^{6} a + \frac {21}{11} x^{11} b^{5} a^{2} + \frac {7}{2} x^{10} b^{4} a^{3} + \frac {35}{9} x^{9} b^{3} a^{4} + \frac {21}{8} x^{8} b^{2} a^{5} + x^{7} b a^{6} + \frac {1}{6} x^{6} a^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.08, size = 78, normalized size = 0.81 \begin {gather*} \frac {1}{13} \, b^{7} x^{13} + \frac {7}{12} \, a b^{6} x^{12} + \frac {21}{11} \, a^{2} b^{5} x^{11} + \frac {7}{2} \, a^{3} b^{4} x^{10} + \frac {35}{9} \, a^{4} b^{3} x^{9} + \frac {21}{8} \, a^{5} b^{2} x^{8} + a^{6} b x^{7} + \frac {1}{6} \, a^{7} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 79, normalized size = 0.82 \begin {gather*} \frac {1}{13} b^{7} x^{13}+\frac {7}{12} a \,b^{6} x^{12}+\frac {21}{11} a^{2} b^{5} x^{11}+\frac {7}{2} a^{3} b^{4} x^{10}+\frac {35}{9} a^{4} b^{3} x^{9}+\frac {21}{8} a^{5} b^{2} x^{8}+a^{6} b \,x^{7}+\frac {1}{6} a^{7} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.39, size = 78, normalized size = 0.81 \begin {gather*} \frac {1}{13} \, b^{7} x^{13} + \frac {7}{12} \, a b^{6} x^{12} + \frac {21}{11} \, a^{2} b^{5} x^{11} + \frac {7}{2} \, a^{3} b^{4} x^{10} + \frac {35}{9} \, a^{4} b^{3} x^{9} + \frac {21}{8} \, a^{5} b^{2} x^{8} + a^{6} b x^{7} + \frac {1}{6} \, a^{7} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 78, normalized size = 0.81 \begin {gather*} \frac {a^7\,x^6}{6}+a^6\,b\,x^7+\frac {21\,a^5\,b^2\,x^8}{8}+\frac {35\,a^4\,b^3\,x^9}{9}+\frac {7\,a^3\,b^4\,x^{10}}{2}+\frac {21\,a^2\,b^5\,x^{11}}{11}+\frac {7\,a\,b^6\,x^{12}}{12}+\frac {b^7\,x^{13}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 90, normalized size = 0.94 \begin {gather*} \frac {a^{7} x^{6}}{6} + a^{6} b x^{7} + \frac {21 a^{5} b^{2} x^{8}}{8} + \frac {35 a^{4} b^{3} x^{9}}{9} + \frac {7 a^{3} b^{4} x^{10}}{2} + \frac {21 a^{2} b^{5} x^{11}}{11} + \frac {7 a b^{6} x^{12}}{12} + \frac {b^{7} x^{13}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________