Optimal. Leaf size=47 \[ \frac {a^2 (a+b x)^8}{8 b^3}+\frac {(a+b x)^{10}}{10 b^3}-\frac {2 a (a+b x)^9}{9 b^3} \]
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Rubi [A] time = 0.02, antiderivative size = 47, 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 {a^2 (a+b x)^8}{8 b^3}+\frac {(a+b x)^{10}}{10 b^3}-\frac {2 a (a+b x)^9}{9 b^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^2 (a+b x)^7 \, dx &=\int \left (\frac {a^2 (a+b x)^7}{b^2}-\frac {2 a (a+b x)^8}{b^2}+\frac {(a+b x)^9}{b^2}\right ) \, dx\\ &=\frac {a^2 (a+b x)^8}{8 b^3}-\frac {2 a (a+b x)^9}{9 b^3}+\frac {(a+b x)^{10}}{10 b^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 93, normalized size = 1.98 \begin {gather*} \frac {a^7 x^3}{3}+\frac {7}{4} a^6 b x^4+\frac {21}{5} a^5 b^2 x^5+\frac {35}{6} a^4 b^3 x^6+5 a^3 b^4 x^7+\frac {21}{8} a^2 b^5 x^8+\frac {7}{9} a b^6 x^9+\frac {b^7 x^{10}}{10} \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^2 (a+b x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.11, size = 79, normalized size = 1.68 \begin {gather*} \frac {1}{10} x^{10} b^{7} + \frac {7}{9} x^{9} b^{6} a + \frac {21}{8} x^{8} b^{5} a^{2} + 5 x^{7} b^{4} a^{3} + \frac {35}{6} x^{6} b^{3} a^{4} + \frac {21}{5} x^{5} b^{2} a^{5} + \frac {7}{4} x^{4} b a^{6} + \frac {1}{3} x^{3} a^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 79, normalized size = 1.68 \begin {gather*} \frac {1}{10} \, b^{7} x^{10} + \frac {7}{9} \, a b^{6} x^{9} + \frac {21}{8} \, a^{2} b^{5} x^{8} + 5 \, a^{3} b^{4} x^{7} + \frac {35}{6} \, a^{4} b^{3} x^{6} + \frac {21}{5} \, a^{5} b^{2} x^{5} + \frac {7}{4} \, a^{6} b x^{4} + \frac {1}{3} \, a^{7} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 80, normalized size = 1.70 \begin {gather*} \frac {1}{10} b^{7} x^{10}+\frac {7}{9} a \,b^{6} x^{9}+\frac {21}{8} a^{2} b^{5} x^{8}+5 a^{3} b^{4} x^{7}+\frac {35}{6} a^{4} b^{3} x^{6}+\frac {21}{5} a^{5} b^{2} x^{5}+\frac {7}{4} a^{6} b \,x^{4}+\frac {1}{3} a^{7} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 79, normalized size = 1.68 \begin {gather*} \frac {1}{10} \, b^{7} x^{10} + \frac {7}{9} \, a b^{6} x^{9} + \frac {21}{8} \, a^{2} b^{5} x^{8} + 5 \, a^{3} b^{4} x^{7} + \frac {35}{6} \, a^{4} b^{3} x^{6} + \frac {21}{5} \, a^{5} b^{2} x^{5} + \frac {7}{4} \, a^{6} b x^{4} + \frac {1}{3} \, a^{7} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 31, normalized size = 0.66 \begin {gather*} \frac {{\left (a+b\,x\right )}^8\,\left (8\,a^2-64\,a\,b\,x+288\,b^2\,x^2\right )}{2880\,b^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 92, normalized size = 1.96 \begin {gather*} \frac {a^{7} x^{3}}{3} + \frac {7 a^{6} b x^{4}}{4} + \frac {21 a^{5} b^{2} x^{5}}{5} + \frac {35 a^{4} b^{3} x^{6}}{6} + 5 a^{3} b^{4} x^{7} + \frac {21 a^{2} b^{5} x^{8}}{8} + \frac {7 a b^{6} x^{9}}{9} + \frac {b^{7} x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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