Optimal. Leaf size=14 \[ \frac {(c+d x)^3}{3 d} \]
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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)^3}{3 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (c+d x)^2 \, dx &=\frac {(c+d x)^3}{3 d}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(c+d x)^3}{3 d} \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.60, size = 18, normalized size = 1.29 \begin {gather*} x \left (c^2+c d x+\frac {d^2 x^2}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 13, normalized size = 0.93
method | result | size |
default | \(\frac {\left (d x +c \right )^{3}}{3 d}\) | \(13\) |
gosper | \(\frac {1}{3} d^{2} x^{3}+c d \,x^{2}+c^{2} x\) | \(21\) |
norman | \(\frac {1}{3} d^{2} x^{3}+c d \,x^{2}+c^{2} x\) | \(21\) |
risch | \(\frac {d^{2} x^{3}}{3}+c d \,x^{2}+c^{2} x +\frac {c^{3}}{3 d}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} \, d^{2} x^{3} + c d x^{2} + c^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.28, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} \, d^{2} x^{3} + c d x^{2} + c^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 19 vs.
\(2 (8) = 16\).
time = 0.03, size = 19, normalized size = 1.36 \begin {gather*} c^{2} x + c d x^{2} + \frac {d^{2} x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {\left (d x+c\right )^{3}}{3 d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 20, normalized size = 1.43 \begin {gather*} c^2\,x+c\,d\,x^2+\frac {d^2\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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