Optimal. Leaf size=14 \[ \frac{(a x+b)^4}{4 a} \]
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Rubi [A] time = 0.0040203, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 32} \[ \frac{(a x+b)^4}{4 a} \]
Antiderivative was successfully verified.
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Rule 263
Rule 32
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^3 x^3 \, dx &=\int (b+a x)^3 \, dx\\ &=\frac{(b+a x)^4}{4 a}\\ \end{align*}
Mathematica [A] time = 0.0013089, size = 14, normalized size = 1. \[ \frac{(a x+b)^4}{4 a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( ax+b \right ) ^{4}}{4\,a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01474, size = 42, normalized size = 3. \begin{align*} \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.3958, size = 66, normalized size = 4.71 \begin{align*} \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.060989, size = 32, normalized size = 2.29 \begin{align*} \frac{a^{3} x^{4}}{4} + a^{2} b x^{3} + \frac{3 a b^{2} x^{2}}{2} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.12127, size = 42, normalized size = 3. \begin{align*} \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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