Optimal. Leaf size=14 \[ \frac {(a+b x)^3}{3 b} \]
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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 {(a+b x)^3}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (a+b x)^2 \, dx &=\frac {(a+b x)^3}{3 b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^3}{3 b} \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 | \(\frac {\left (b x +a \right )^{3}}{3 b}\) | \(13\) |
gosper | \(\frac {1}{3} b^{2} x^{3}+a b \,x^{2}+a^{2} x\) | \(21\) |
norman | \(\frac {1}{3} b^{2} x^{3}+a b \,x^{2}+a^{2} x\) | \(21\) |
risch | \(\frac {b^{2} x^{3}}{3}+a b \,x^{2}+a^{2} x +\frac {a^{3}}{3 b}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} \, b^{2} x^{3} + a b x^{2} + a^{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 = 0.01, size = 19, normalized size = 1.36 \begin {gather*} a^{2} x + a b x^{2} + \frac {b^{2} x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.73, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{3}}{3 \, b} \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*} a^2\,x+a\,b\,x^2+\frac {b^2\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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