Optimal. Leaf size=14 \[ \frac {(a+b x)^8}{8 b} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {27, 32} \begin {gather*} \frac {(a+b x)^8}{8 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 )^3 \, dx &=\int (a+b x)^7 \, dx\\ &=\frac {(a+b x)^8}{8 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^8}{8 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 )^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.38, size = 75, normalized size = 5.36 \begin {gather*} \frac {1}{8} x^{8} b^{7} + x^{7} b^{6} a + \frac {7}{2} x^{6} b^{5} a^{2} + 7 x^{5} b^{4} a^{3} + \frac {35}{4} x^{4} b^{3} a^{4} + 7 x^{3} b^{2} a^{5} + \frac {7}{2} x^{2} b a^{6} + x a^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 71, normalized size = 5.07 \begin {gather*} \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} a^{6} + \frac {3}{4} \, {\left (b x^{2} + 2 \, a x\right )}^{2} a^{4} b + \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )}^{3} a^{2} b^{2} + \frac {1}{8} \, {\left (b x^{2} + 2 \, a x\right )}^{4} b^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 76, normalized size = 5.43 \begin {gather*} \frac {1}{8} b^{7} x^{8}+a \,b^{6} x^{7}+\frac {7}{2} a^{2} b^{5} x^{6}+7 a^{3} b^{4} x^{5}+\frac {35}{4} a^{4} b^{3} x^{4}+7 a^{5} b^{2} x^{3}+\frac {7}{2} a^{6} b \,x^{2}+a^{7} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 23, normalized size = 1.64 \begin {gather*} \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{4}}{8 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 75, normalized size = 5.36 \begin {gather*} a^7\,x+\frac {7\,a^6\,b\,x^2}{2}+7\,a^5\,b^2\,x^3+\frac {35\,a^4\,b^3\,x^4}{4}+7\,a^3\,b^4\,x^5+\frac {7\,a^2\,b^5\,x^6}{2}+a\,b^6\,x^7+\frac {b^7\,x^8}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 83, normalized size = 5.93 \begin {gather*} a^{7} x + \frac {7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac {35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac {7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac {b^{7} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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