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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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^5}{(a c+b c x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.22, 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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giac [A] time = 1.09, 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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maple [A] time = 0.00, size = 16, normalized size = 1.07 \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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maxima [A] time = 1.33, 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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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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sympy [A] time = 0.20, 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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