Optimal. Leaf size=14 \[ \frac {(a+b x)^4}{4 b} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {27, 32} \begin {gather*} \frac {(a+b x)^4}{4 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin {align*} \int (a+b x) \left (a^2+2 a b x+b^2 x^2\right ) \, dx &=\int (a+b x)^3 \, dx\\ &=\frac {(a+b x)^4}{4 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^4}{4 b} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b x) \left (a^2+2 a b x+b^2 x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.37, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{4} x^{4} b^{3} + x^{3} b^{2} a + \frac {3}{2} x^{2} b a^{2} + x a^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 31, normalized size = 2.21 \begin {gather*} \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} a^{2} + \frac {1}{4} \, {\left (b x^{2} + 2 \, a x\right )}^{2} b \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 32, normalized size = 2.29 \begin {gather*} \frac {1}{4} b^{3} x^{4}+a \,b^{2} x^{3}+\frac {3}{2} a^{2} b \,x^{2}+a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 23, normalized size = 1.64 \begin {gather*} \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{2}}{4 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 31, normalized size = 2.21 \begin {gather*} a^3\,x+\frac {3\,a^2\,b\,x^2}{2}+a\,b^2\,x^3+\frac {b^3\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 32, normalized size = 2.29 \begin {gather*} a^{3} x + \frac {3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac {b^{3} x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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