Optimal. Leaf size=24 \[ \frac {c (a+b x)^2}{2 b}+\frac {d x^2}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {c (a+b x)^2}{2 b}+\frac {d x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int (d x+c (a+b x)) \, dx &=\frac {d x^2}{2}+\frac {c (a+b x)^2}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 0.92 \begin {gather*} a c x+\frac {1}{2} b c x^2+\frac {d x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (d x+c (a+b x)) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.00, size = 18, normalized size = 0.75 \begin {gather*} \frac {1}{2} x^{2} c b + \frac {1}{2} x^{2} d + x c a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 20, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, d x^{2} + \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 = 20, normalized size = 0.83 \begin {gather*} \frac {d \,x^{2}}{2}+\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 = 0.57, size = 20, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, d x^{2} + \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 = 17, normalized size = 0.71 \begin {gather*} \left (\frac {d}{2}+\frac {b\,c}{2}\right )\,x^2+a\,c\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 15, normalized size = 0.62 \begin {gather*} a c x + x^{2} \left (\frac {b c}{2} + \frac {d}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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