Optimal. Leaf size=12 \[ a x+\frac {b x^2}{2} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14}
\begin {gather*} a x+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a x^2+b x^3}{x^2} \, dx &=\int (a+b x) \, dx\\ &=a x+\frac {b x^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} a x+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.92
method | result | size |
gosper | \(\frac {x \left (b x +2 a \right )}{2}\) | \(11\) |
default | \(a x +\frac {1}{2} b \,x^{2}\) | \(11\) |
risch | \(a x +\frac {1}{2} b \,x^{2}\) | \(11\) |
norman | \(\frac {a \,x^{2}+\frac {1}{2} b \,x^{3}}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.59, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.67 \begin {gather*} a x + \frac {b x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.47, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} \frac {b\,x^2}{2}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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