Optimal. Leaf size=28 \[ a x+\frac {b x^2}{2}+\frac {c x^3}{3}+\frac {d x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} a x+\frac {b x^2}{2}+\frac {c x^3}{3}+\frac {d x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (a+b x+c x^2+d x^3\right ) \, dx &=a x+\frac {b x^2}{2}+\frac {c x^3}{3}+\frac {d x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} a x+\frac {b x^2}{2}+\frac {c x^3}{3}+\frac {d x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 23, normalized size = 0.82
method | result | size |
gosper | \(a x +\frac {1}{2} x^{2} b +\frac {1}{3} c \,x^{3}+\frac {1}{4} d \,x^{4}\) | \(23\) |
default | \(a x +\frac {1}{2} x^{2} b +\frac {1}{3} c \,x^{3}+\frac {1}{4} d \,x^{4}\) | \(23\) |
norman | \(a x +\frac {1}{2} x^{2} b +\frac {1}{3} c \,x^{3}+\frac {1}{4} d \,x^{4}\) | \(23\) |
risch | \(a x +\frac {1}{2} x^{2} b +\frac {1}{3} c \,x^{3}+\frac {1}{4} d \,x^{4}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{4} \, d x^{4} + \frac {1}{3} \, c x^{3} + \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 = 1.13, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{4} \, d x^{4} + \frac {1}{3} \, c x^{3} + \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 = 22, normalized size = 0.79 \begin {gather*} a x + \frac {b x^{2}}{2} + \frac {c x^{3}}{3} + \frac {d x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.91, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{4} \, d x^{4} + \frac {1}{3} \, c x^{3} + \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 = 0.04, size = 22, normalized size = 0.79 \begin {gather*} \frac {d\,x^4}{4}+\frac {c\,x^3}{3}+\frac {b\,x^2}{2}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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