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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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.25, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} x^{3} d^{2} + x^{2} d c + x c^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, 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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maple [A] time = 0.00, size = 13, normalized size = 0.93 \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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maxima [A] time = 1.31, 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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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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sympy [B] time = 0.06, 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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