Optimal. Leaf size=14 \[ \frac {(c+d x)^4}{4 d} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {626, 32} \begin {gather*} \frac {(c+d x)^4}{4 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 626
Rubi steps
\begin {align*} \int \frac {\left (a c+(b c+a d) x+b d x^2\right )^3}{(a+b x)^3} \, dx &=\int (c+d x)^3 \, dx\\ &=\frac {(c+d x)^4}{4 d}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(c+d x)^4}{4 d} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.06, size = 14, normalized size = 1.00 \begin {gather*} \frac {(c+d x)^4}{4 d} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.38, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac {3}{2} \, c^{2} d x^{2} + c^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.17, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac {3}{2} \, c^{2} d x^{2} + c^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 0.93 \begin {gather*} \frac {\left (d x +c \right )^{4}}{4 d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.05, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac {3}{2} \, c^{2} d x^{2} + c^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 31, normalized size = 2.21 \begin {gather*} c^3\,x+\frac {3\,c^2\,d\,x^2}{2}+c\,d^2\,x^3+\frac {d^3\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 32, normalized size = 2.29 \begin {gather*} c^{3} x + \frac {3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac {d^{3} x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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