Optimal. Leaf size=30 \[ \frac {a}{6 b^2 (a+b x)^6}-\frac {1}{5 b^2 (a+b x)^5} \]
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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}{6 b^2 (a+b x)^6}-\frac {1}{5 b^2 (a+b x)^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {x}{(a+b x)^7} \, dx &=\int \left (-\frac {a}{b (a+b x)^7}+\frac {1}{b (a+b x)^6}\right ) \, dx\\ &=\frac {a}{6 b^2 (a+b x)^6}-\frac {1}{5 b^2 (a+b x)^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.67 \begin {gather*} -\frac {a+6 b x}{30 b^2 (a+b x)^6} \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 {x}{(a+b x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.88, size = 76, normalized size = 2.53 \begin {gather*} -\frac {6 \, b x + a}{30 \, {\left (b^{8} x^{6} + 6 \, a b^{7} x^{5} + 15 \, a^{2} b^{6} x^{4} + 20 \, a^{3} b^{5} x^{3} + 15 \, a^{4} b^{4} x^{2} + 6 \, a^{5} b^{3} x + a^{6} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.39, size = 18, normalized size = 0.60 \begin {gather*} -\frac {6 \, b x + a}{30 \, {\left (b x + a\right )}^{6} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {a}{6 \left (b x +a \right )^{6} b^{2}}-\frac {1}{5 \left (b x +a \right )^{5} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.37, size = 76, normalized size = 2.53 \begin {gather*} -\frac {6 \, b x + a}{30 \, {\left (b^{8} x^{6} + 6 \, a b^{7} x^{5} + 15 \, a^{2} b^{6} x^{4} + 20 \, a^{3} b^{5} x^{3} + 15 \, a^{4} b^{4} x^{2} + 6 \, a^{5} b^{3} x + a^{6} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 18, normalized size = 0.60 \begin {gather*} -\frac {a+6\,b\,x}{30\,b^2\,{\left (a+b\,x\right )}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.50, size = 80, normalized size = 2.67 \begin {gather*} \frac {- a - 6 b x}{30 a^{6} b^{2} + 180 a^{5} b^{3} x + 450 a^{4} b^{4} x^{2} + 600 a^{3} b^{5} x^{3} + 450 a^{2} b^{6} x^{4} + 180 a b^{7} x^{5} + 30 b^{8} x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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