Optimal. Leaf size=15 \[ -\frac {1}{b c^7 (a+b x)} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {21, 32}
\begin {gather*} -\frac {1}{b c^7 (a+b x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{(a c+b c x)^7} \, dx &=\frac {\int \frac {1}{(a+b x)^2} \, dx}{c^7}\\ &=-\frac {1}{b c^7 (a+b x)}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{b c^7 (a+b x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 16, normalized size = 1.07
method | result | size |
gosper | \(-\frac {1}{b \,c^{7} \left (b x +a \right )}\) | \(16\) |
default | \(-\frac {1}{b \,c^{7} \left (b x +a \right )}\) | \(16\) |
risch | \(-\frac {1}{b \,c^{7} \left (b x +a \right )}\) | \(16\) |
norman | \(\frac {-\frac {a^{5}}{b c}-\frac {b^{4} x^{5}}{c}-\frac {5 a^{4} x}{c}-\frac {5 a \,b^{3} x^{4}}{c}-\frac {10 b^{2} a^{2} x^{3}}{c}-\frac {10 a^{3} b \,x^{2}}{c}}{c^{6} \left (b x +a \right )^{6}}\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 19, normalized size = 1.27 \begin {gather*} -\frac {1}{b^{2} c^{7} x + a b c^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 19, normalized size = 1.27 \begin {gather*} -\frac {1}{b^{2} c^{7} x + a b c^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 17, normalized size = 1.13 \begin {gather*} - \frac {1}{a b c^{7} + b^{2} c^{7} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.79, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{{\left (b x + a\right )} b c^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 19, normalized size = 1.27 \begin {gather*} -\frac {1}{x\,b^2\,c^7+a\,b\,c^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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