Optimal. Leaf size=25 \[ \frac {a x^3}{3}+\frac {b x^4}{4}+\frac {c x^5}{5} \]
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Rubi [A] time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {a x^3}{3}+\frac {b x^4}{4}+\frac {c x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (a x^2+b x^3+c x^4\right ) \, dx &=\frac {a x^3}{3}+\frac {b x^4}{4}+\frac {c x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} \frac {a x^3}{3}+\frac {b x^4}{4}+\frac {c x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a x^2+b x^3+c x^4\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.84, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{5} x^{5} c + \frac {1}{4} x^{4} b + \frac {1}{3} x^{3} a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.54, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{4} \, b x^{4} + \frac {1}{3} \, a x^{3} \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 = 0.80 \begin {gather*} \frac {1}{5} c \,x^{5}+\frac {1}{4} b \,x^{4}+\frac {1}{3} a \,x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{4} \, b x^{4} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^3\,\left (12\,c\,x^2+15\,b\,x+20\,a\right )}{60} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.76 \begin {gather*} \frac {a x^{3}}{3} + \frac {b x^{4}}{4} + \frac {c x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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