Optimal. Leaf size=56 \[ -\frac {b^2 (a+b x)^7}{252 a^3 x^7}+\frac {b (a+b x)^7}{36 a^2 x^8}-\frac {(a+b x)^7}{9 a x^9} \]
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Rubi [A] time = 0.01, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {45, 37} \begin {gather*} -\frac {b^2 (a+b x)^7}{252 a^3 x^7}+\frac {b (a+b x)^7}{36 a^2 x^8}-\frac {(a+b x)^7}{9 a x^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^6}{x^{10}} \, dx &=-\frac {(a+b x)^7}{9 a x^9}-\frac {(2 b) \int \frac {(a+b x)^6}{x^9} \, dx}{9 a}\\ &=-\frac {(a+b x)^7}{9 a x^9}+\frac {b (a+b x)^7}{36 a^2 x^8}+\frac {b^2 \int \frac {(a+b x)^6}{x^8} \, dx}{36 a^2}\\ &=-\frac {(a+b x)^7}{9 a x^9}+\frac {b (a+b x)^7}{36 a^2 x^8}-\frac {b^2 (a+b x)^7}{252 a^3 x^7}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 80, normalized size = 1.43 \begin {gather*} -\frac {a^6}{9 x^9}-\frac {3 a^5 b}{4 x^8}-\frac {15 a^4 b^2}{7 x^7}-\frac {10 a^3 b^3}{3 x^6}-\frac {3 a^2 b^4}{x^5}-\frac {3 a b^5}{2 x^4}-\frac {b^6}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^6}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.13, size = 68, normalized size = 1.21 \begin {gather*} -\frac {84 \, b^{6} x^{6} + 378 \, a b^{5} x^{5} + 756 \, a^{2} b^{4} x^{4} + 840 \, a^{3} b^{3} x^{3} + 540 \, a^{4} b^{2} x^{2} + 189 \, a^{5} b x + 28 \, a^{6}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 68, normalized size = 1.21 \begin {gather*} -\frac {84 \, b^{6} x^{6} + 378 \, a b^{5} x^{5} + 756 \, a^{2} b^{4} x^{4} + 840 \, a^{3} b^{3} x^{3} + 540 \, a^{4} b^{2} x^{2} + 189 \, a^{5} b x + 28 \, a^{6}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 69, normalized size = 1.23 \begin {gather*} -\frac {b^{6}}{3 x^{3}}-\frac {3 a \,b^{5}}{2 x^{4}}-\frac {3 a^{2} b^{4}}{x^{5}}-\frac {10 a^{3} b^{3}}{3 x^{6}}-\frac {15 a^{4} b^{2}}{7 x^{7}}-\frac {3 a^{5} b}{4 x^{8}}-\frac {a^{6}}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 68, normalized size = 1.21 \begin {gather*} -\frac {84 \, b^{6} x^{6} + 378 \, a b^{5} x^{5} + 756 \, a^{2} b^{4} x^{4} + 840 \, a^{3} b^{3} x^{3} + 540 \, a^{4} b^{2} x^{2} + 189 \, a^{5} b x + 28 \, a^{6}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 68, normalized size = 1.21 \begin {gather*} -\frac {\frac {a^6}{9}+\frac {3\,a^5\,b\,x}{4}+\frac {15\,a^4\,b^2\,x^2}{7}+\frac {10\,a^3\,b^3\,x^3}{3}+3\,a^2\,b^4\,x^4+\frac {3\,a\,b^5\,x^5}{2}+\frac {b^6\,x^6}{3}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.56, size = 73, normalized size = 1.30 \begin {gather*} \frac {- 28 a^{6} - 189 a^{5} b x - 540 a^{4} b^{2} x^{2} - 840 a^{3} b^{3} x^{3} - 756 a^{2} b^{4} x^{4} - 378 a b^{5} x^{5} - 84 b^{6} x^{6}}{252 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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