Optimal. Leaf size=14 \[ -\frac {1}{6 b (a+b x)^6} \]
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Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32}
\begin {gather*} -\frac {1}{6 b (a+b x)^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(a+b x)^7} \, dx &=-\frac {1}{6 b (a+b x)^6}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{6 b (a+b x)^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 13, normalized size = 0.93
method | result | size |
gosper | \(-\frac {1}{6 b \left (b x +a \right )^{6}}\) | \(13\) |
default | \(-\frac {1}{6 b \left (b x +a \right )^{6}}\) | \(13\) |
norman | \(-\frac {1}{6 b \left (b x +a \right )^{6}}\) | \(13\) |
risch | \(-\frac {1}{6 b \left (b x +a \right )^{6}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{6 \, {\left (b x + a\right )}^{6} b} \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. 68 vs.
\(2 (12) = 24\).
time = 0.81, size = 68, normalized size = 4.86 \begin {gather*} -\frac {1}{6 \, {\left (b^{7} x^{6} + 6 \, a b^{6} x^{5} + 15 \, a^{2} b^{5} x^{4} + 20 \, a^{3} b^{4} x^{3} + 15 \, a^{4} b^{3} x^{2} + 6 \, a^{5} b^{2} x + a^{6} b\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. 73 vs.
\(2 (12) = 24\).
time = 0.18, size = 73, normalized size = 5.21 \begin {gather*} - \frac {1}{6 a^{6} b + 36 a^{5} b^{2} x + 90 a^{4} b^{3} x^{2} + 120 a^{3} b^{4} x^{3} + 90 a^{2} b^{5} x^{4} + 36 a b^{6} x^{5} + 6 b^{7} x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.50, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{6 \, {\left (b x + a\right )}^{6} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 70, normalized size = 5.00 \begin {gather*} -\frac {1}{6\,a^6\,b+36\,a^5\,b^2\,x+90\,a^4\,b^3\,x^2+120\,a^3\,b^4\,x^3+90\,a^2\,b^5\,x^4+36\,a\,b^6\,x^5+6\,b^7\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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