Optimal. Leaf size=30 \[ \frac {(a+b x)^9}{9 b^2}-\frac {a (a+b x)^8}{8 b^2} \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \begin {gather*} \frac {(a+b x)^9}{9 b^2}-\frac {a (a+b x)^8}{8 b^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x (a+b x)^7 \, dx &=\int \left (-\frac {a (a+b x)^7}{b}+\frac {(a+b x)^8}{b}\right ) \, dx\\ &=-\frac {a (a+b x)^8}{8 b^2}+\frac {(a+b x)^9}{9 b^2}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 91, normalized size = 3.03 \begin {gather*} \frac {a^7 x^2}{2}+\frac {7}{3} a^6 b x^3+\frac {21}{4} a^5 b^2 x^4+7 a^4 b^3 x^5+\frac {35}{6} a^3 b^4 x^6+3 a^2 b^5 x^7+\frac {7}{8} a b^6 x^8+\frac {b^7 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x (a+b x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.00, size = 79, normalized size = 2.63 \begin {gather*} \frac {1}{9} x^{9} b^{7} + \frac {7}{8} x^{8} b^{6} a + 3 x^{7} b^{5} a^{2} + \frac {35}{6} x^{6} b^{4} a^{3} + 7 x^{5} b^{3} a^{4} + \frac {21}{4} x^{4} b^{2} a^{5} + \frac {7}{3} x^{3} b a^{6} + \frac {1}{2} x^{2} a^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.92, size = 79, normalized size = 2.63 \begin {gather*} \frac {1}{9} \, b^{7} x^{9} + \frac {7}{8} \, a b^{6} x^{8} + 3 \, a^{2} b^{5} x^{7} + \frac {35}{6} \, a^{3} b^{4} x^{6} + 7 \, a^{4} b^{3} x^{5} + \frac {21}{4} \, a^{5} b^{2} x^{4} + \frac {7}{3} \, a^{6} b x^{3} + \frac {1}{2} \, a^{7} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 80, normalized size = 2.67 \begin {gather*} \frac {1}{9} b^{7} x^{9}+\frac {7}{8} a \,b^{6} x^{8}+3 a^{2} b^{5} x^{7}+\frac {35}{6} a^{3} b^{4} x^{6}+7 a^{4} b^{3} x^{5}+\frac {21}{4} a^{5} b^{2} x^{4}+\frac {7}{3} a^{6} b \,x^{3}+\frac {1}{2} a^{7} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.35, size = 79, normalized size = 2.63 \begin {gather*} \frac {1}{9} \, b^{7} x^{9} + \frac {7}{8} \, a b^{6} x^{8} + 3 \, a^{2} b^{5} x^{7} + \frac {35}{6} \, a^{3} b^{4} x^{6} + 7 \, a^{4} b^{3} x^{5} + \frac {21}{4} \, a^{5} b^{2} x^{4} + \frac {7}{3} \, a^{6} b x^{3} + \frac {1}{2} \, a^{7} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 25, normalized size = 0.83 \begin {gather*} -\frac {2\,\left (\frac {a\,{\left (a+b\,x\right )}^8}{16}-\frac {{\left (a+b\,x\right )}^9}{18}\right )}{b^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 90, normalized size = 3.00 \begin {gather*} \frac {a^{7} x^{2}}{2} + \frac {7 a^{6} b x^{3}}{3} + \frac {21 a^{5} b^{2} x^{4}}{4} + 7 a^{4} b^{3} x^{5} + \frac {35 a^{3} b^{4} x^{6}}{6} + 3 a^{2} b^{5} x^{7} + \frac {7 a b^{6} x^{8}}{8} + \frac {b^{7} x^{9}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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