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 = {45}
\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 45
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 = 0.00, 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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Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(30)=60\).
time = 2.43, size = 75, normalized size = 2.50 \begin {gather*} \frac {-a-6 b x}{30 b^2 \left (a^6+6 a^5 b x+15 a^4 b^2 x^2+20 a^3 b^3 x^3+15 a^2 b^4 x^4+6 a b^5 x^5+b^6 x^6\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 0.90
method | result | size |
gosper | \(-\frac {6 b x +a}{30 \left (b x +a \right )^{6} b^{2}}\) | \(19\) |
norman | \(\frac {-\frac {x}{5 b}-\frac {a}{30 b^{2}}}{\left (b x +a \right )^{6}}\) | \(22\) |
risch | \(\frac {-\frac {x}{5 b}-\frac {a}{30 b^{2}}}{\left (b x +a \right )^{6}}\) | \(22\) |
default | \(\frac {a}{6 b^{2} \left (b x +a \right )^{6}}-\frac {1}{5 b^{2} \left (b x +a \right )^{5}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 76 vs.
\(2 (26) = 52\).
time = 0.24, 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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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 76 vs.
\(2 (26) = 52\).
time = 0.30, 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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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 80 vs.
\(2 (26) = 52\).
time = 0.21, 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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Giac [A]
time = 0.00, size = 22, normalized size = 0.73 \begin {gather*} \frac {-6 x b-a}{30 b^{2} \left (x b+a\right )^{6}} \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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