Optimal. Leaf size=14 \[ \frac {(c+d x)^4}{4 d} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} \frac {(c+d x)^4}{4 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \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 [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.18, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{4} x^{4} d^{3} + x^{3} d^{2} c + \frac {3}{2} x^{2} d c^{2} + x c^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 12, normalized size = 0.86 \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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maple [A] time = 0.00, 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 = 1.35, 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 = 0.04, 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 = 0.06, 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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