Optimal. Leaf size=14 \[ \frac {(a+b x)^{11}}{11 b} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} \frac {(a+b x)^{11}}{11 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (a+b x)^{10} \, dx &=\frac {(a+b x)^{11}}{11 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^{11}}{11 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)^{10} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.26, size = 108, normalized size = 7.71 \begin {gather*} \frac {1}{11} x^{11} b^{10} + x^{10} b^{9} a + 5 x^{9} b^{8} a^{2} + 15 x^{8} b^{7} a^{3} + 30 x^{7} b^{6} a^{4} + 42 x^{6} b^{5} a^{5} + 42 x^{5} b^{4} a^{6} + 30 x^{4} b^{3} a^{7} + 15 x^{3} b^{2} a^{8} + 5 x^{2} b a^{9} + x a^{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{11}}{11 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} \frac {\left (b x +a \right )^{11}}{11 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{11}}{11 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 108, normalized size = 7.71 \begin {gather*} a^{10}\,x+5\,a^9\,b\,x^2+15\,a^8\,b^2\,x^3+30\,a^7\,b^3\,x^4+42\,a^6\,b^4\,x^5+42\,a^5\,b^5\,x^6+30\,a^4\,b^6\,x^7+15\,a^3\,b^7\,x^8+5\,a^2\,b^8\,x^9+a\,b^9\,x^{10}+\frac {b^{10}\,x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 114, normalized size = 8.14 \begin {gather*} a^{10} x + 5 a^{9} b x^{2} + 15 a^{8} b^{2} x^{3} + 30 a^{7} b^{3} x^{4} + 42 a^{6} b^{4} x^{5} + 42 a^{5} b^{5} x^{6} + 30 a^{4} b^{6} x^{7} + 15 a^{3} b^{7} x^{8} + 5 a^{2} b^{8} x^{9} + a b^{9} x^{10} + \frac {b^{10} x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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