Optimal. Leaf size=12 \[ -\frac {1}{b (a+b x)} \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 32} \[ -\frac {1}{b (a+b x)} \]
Antiderivative was successfully verified.
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Rule 32
Rule 1584
Rubi steps
\begin {align*} \int \frac {x^4}{\left (a x^2+b x^3\right )^2} \, dx &=\int \frac {1}{(a+b x)^2} \, dx\\ &=-\frac {1}{b (a+b x)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ -\frac {1}{b (a+b x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 13, normalized size = 1.08 \[ -\frac {1}{b^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 12, normalized size = 1.00 \[ -\frac {1}{{\left (b x + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 13, normalized size = 1.08 \[ -\frac {1}{\left (b x +a \right ) b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 13, normalized size = 1.08 \[ -\frac {1}{b^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.17, size = 12, normalized size = 1.00 \[ -\frac {1}{b\,\left (a+b\,x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 10, normalized size = 0.83 \[ - \frac {1}{a b + b^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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