Optimal. Leaf size=15 \[ \frac {c (a+b x)^2}{2 b} \]
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Rubi [A] time = 0.00, antiderivative size = 15, 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 = {9} \begin {gather*} \frac {c (a+b x)^2}{2 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {align*} \int c (a+b x) \, dx &=\frac {c (a+b x)^2}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} c \left (a x+\frac {b x^2}{2}\right ) \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 (a+b x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.49, size = 12, normalized size = 0.80 \begin {gather*} \frac {1}{2} x^{2} c b + x c a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} c \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 = 0.87 \begin {gather*} \left (\frac {1}{2} b \,x^{2}+a x \right ) c \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} c \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.73 \begin {gather*} \frac {c\,x\,\left (2\,a+b\,x\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 0.80 \begin {gather*} a c x + \frac {b c x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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