Optimal. Leaf size=17 \[ \frac {b^5 (c+d x)^3}{3 d^6} \]
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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} \[ \frac {b^5 (c+d x)^3}{3 d^6} \]
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {\left (\frac {b c}{d}+b x\right )^5}{(c+d x)^3} \, dx &=\frac {b^5 \int (c+d x)^2 \, dx}{d^5}\\ &=\frac {b^5 (c+d x)^3}{3 d^6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {b^5 (c+d x)^3}{3 d^6} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 35, normalized size = 2.06 \[ \frac {b^{5} d^{2} x^{3} + 3 \, b^{5} c d x^{2} + 3 \, b^{5} c^{2} x}{3 \, d^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.01, size = 35, normalized size = 2.06 \[ \frac {b^{5} d^{2} x^{3} + 3 \, b^{5} c d x^{2} + 3 \, b^{5} c^{2} x}{3 \, d^{5}} \]
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 \[ \frac {\left (d x +c \right )^{3} b^{5}}{3 d^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.37, size = 35, normalized size = 2.06 \[ \frac {b^{5} d^{2} x^{3} + 3 \, b^{5} c d x^{2} + 3 \, b^{5} c^{2} x}{3 \, d^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 27, normalized size = 1.59 \[ \frac {b^5\,x\,\left (3\,c^2+3\,c\,d\,x+d^2\,x^2\right )}{3\,d^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 34, normalized size = 2.00 \[ \frac {b^{5} c^{2} x}{d^{5}} + \frac {b^{5} c x^{2}}{d^{4}} + \frac {b^{5} x^{3}}{3 d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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