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 = 0.0134989, antiderivative size = 30, normalized size of antiderivative = 1., 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} \[ \frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5} \]
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*}
Mathematica [A] time = 0.0105081, size = 20, normalized size = 0.67 \[ -\frac{a+6 b x}{30 b^2 (a+b x)^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 0.9 \begin{align*}{\frac{a}{6\,{b}^{2} \left ( bx+a \right ) ^{6}}}-{\frac{1}{5\,{b}^{2} \left ( bx+a \right ) ^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.08307, size = 103, normalized size = 3.43 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.51044, size = 159, normalized size = 5.3 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.77669, size = 80, normalized size = 2.67 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20376, size = 24, normalized size = 0.8 \begin{align*} -\frac{6 \, b x + a}{30 \,{\left (b x + a\right )}^{6} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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