Optimal. Leaf size=8 \[ \frac {b^3 x}{d^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 8, 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, 8}
\begin {gather*} \frac {b^3 x}{d^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 21
Rubi steps
\begin {align*} \int \frac {\left (\frac {b c}{d}+b x\right )^3}{(c+d x)^3} \, dx &=\frac {b^3 \int 1 \, dx}{d^3}\\ &=\frac {b^3 x}{d^3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {b^3 x}{d^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 9, normalized size = 1.12
method | result | size |
default | \(\frac {b^{3} x}{d^{3}}\) | \(9\) |
risch | \(\frac {b^{3} x}{d^{3}}\) | \(9\) |
norman | \(\frac {b^{3} d \,x^{3}-\frac {2 c^{3} b^{3}}{d^{2}}-\frac {3 c^{2} b^{3} x}{d}}{d^{2} \left (d x +c \right )^{2}}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 8, normalized size = 1.00 \begin {gather*} \frac {b^{3} x}{d^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 8, normalized size = 1.00 \begin {gather*} \frac {b^{3} x}{d^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.88 \begin {gather*} \frac {b^{3} x}{d^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.53, size = 8, normalized size = 1.00 \begin {gather*} \frac {b^{3} x}{d^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 8, normalized size = 1.00 \begin {gather*} \frac {b^3\,x}{d^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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