Optimal. Leaf size=30 \[ \frac {(a+b x)^5}{5 b^2}-\frac {a (a+b x)^4}{4 b^2} \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \begin {gather*} \frac {(a+b x)^5}{5 b^2}-\frac {a (a+b x)^4}{4 b^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x (a+b x)^3 \, dx &=\int \left (-\frac {a (a+b x)^3}{b}+\frac {(a+b x)^4}{b}\right ) \, dx\\ &=-\frac {a (a+b x)^4}{4 b^2}+\frac {(a+b x)^5}{5 b^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 40, normalized size = 1.33 \begin {gather*} \frac {a^3 x^2}{2}+a^2 b x^3+\frac {3}{4} a b^2 x^4+\frac {b^3 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 x (a+b x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.70, size = 34, normalized size = 1.13 \begin {gather*} \frac {1}{5} x^{5} b^{3} + \frac {3}{4} x^{4} b^{2} a + x^{3} b a^{2} + \frac {1}{2} x^{2} a^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 34, normalized size = 1.13 \begin {gather*} \frac {1}{5} \, b^{3} x^{5} + \frac {3}{4} \, a b^{2} x^{4} + a^{2} b x^{3} + \frac {1}{2} \, a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 1.17 \begin {gather*} \frac {1}{5} b^{3} x^{5}+\frac {3}{4} a \,b^{2} x^{4}+a^{2} b \,x^{3}+\frac {1}{2} a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 34, normalized size = 1.13 \begin {gather*} \frac {1}{5} \, b^{3} x^{5} + \frac {3}{4} \, a b^{2} x^{4} + a^{2} b x^{3} + \frac {1}{2} \, a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 34, normalized size = 1.13 \begin {gather*} \frac {a^3\,x^2}{2}+a^2\,b\,x^3+\frac {3\,a\,b^2\,x^4}{4}+\frac {b^3\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 36, normalized size = 1.20 \begin {gather*} \frac {a^{3} x^{2}}{2} + a^{2} b x^{3} + \frac {3 a b^{2} x^{4}}{4} + \frac {b^{3} x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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