Optimal. Leaf size=23 \[ \frac {b^4 c x}{d^4}+\frac {b^4 x^2}{2 d^3} \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {21} \[ \frac {b^4 c x}{d^4}+\frac {b^4 x^2}{2 d^3} \]
Antiderivative was successfully verified.
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Rule 21
Rubi steps
\begin {align*} \int \frac {\left (\frac {b c}{d}+b x\right )^4}{(c+d x)^3} \, dx &=\frac {b^4 \int (c+d x) \, dx}{d^4}\\ &=\frac {b^4 c x}{d^4}+\frac {b^4 x^2}{2 d^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 0.83 \[ \frac {b^4 \left (c x+\frac {d x^2}{2}\right )}{d^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 21, normalized size = 0.91 \[ \frac {b^{4} d x^{2} + 2 \, b^{4} c x}{2 \, d^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 21, normalized size = 0.91 \[ \frac {b^{4} d x^{2} + 2 \, b^{4} c x}{2 \, d^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ \frac {\left (\frac {1}{2} d \,x^{2}+c x \right ) b^{4}}{d^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 21, normalized size = 0.91 \[ \frac {b^{4} d x^{2} + 2 \, b^{4} c x}{2 \, d^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 16, normalized size = 0.70 \[ \frac {b^4\,x\,\left (2\,c+d\,x\right )}{2\,d^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 0.87 \[ \frac {b^{4} c x}{d^{4}} + \frac {b^{4} x^{2}}{2 d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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