Optimal. Leaf size=17 \[ \frac {b^2 (a+b x)^3}{3 d^3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {21, 32} \[ \frac {b^2 (a+b x)^3}{3 d^3} \]
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{\left (\frac {a d}{b}+d x\right )^3} \, dx &=\frac {b^3 \int (a+b x)^2 \, dx}{d^3}\\ &=\frac {b^2 (a+b x)^3}{3 d^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {b^2 (a+b x)^3}{3 d^3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 31, normalized size = 1.82 \[ \frac {b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x}{3 \, d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.09, size = 31, normalized size = 1.82 \[ \frac {b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x}{3 \, d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {\left (b x +a \right )^{3} b^{2}}{3 d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.37, size = 31, normalized size = 1.82 \[ \frac {b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x}{3 \, d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 27, normalized size = 1.59 \[ \frac {b^3\,x\,\left (3\,a^2+3\,a\,b\,x+b^2\,x^2\right )}{3\,d^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 34, normalized size = 2.00 \[ \frac {a^{2} b^{3} x}{d^{3}} + \frac {a b^{4} x^{2}}{d^{3}} + \frac {b^{5} x^{3}}{3 d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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