Optimal. Leaf size=14 \[ \frac {(c+d x)^8}{8 d} \]
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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 {(c+d x)^8}{8 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (c+d x)^7 \, dx &=\frac {(c+d x)^8}{8 d}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(c+d x)^8}{8 d} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.29, size = 75, normalized size = 5.36 \begin {gather*} \frac {1}{8} x^{8} d^{7} + x^{7} d^{6} c + \frac {7}{2} x^{6} d^{5} c^{2} + 7 x^{5} d^{4} c^{3} + \frac {35}{4} x^{4} d^{3} c^{4} + 7 x^{3} d^{2} c^{5} + \frac {7}{2} x^{2} d c^{6} + x c^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.30, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (d x + c\right )}^{8}}{8 \, d} \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 (d x +c \right )^{8}}{8 d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (d x + c\right )}^{8}}{8 \, d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 75, normalized size = 5.36 \begin {gather*} c^7\,x+\frac {7\,c^6\,d\,x^2}{2}+7\,c^5\,d^2\,x^3+\frac {35\,c^4\,d^3\,x^4}{4}+7\,c^3\,d^4\,x^5+\frac {7\,c^2\,d^5\,x^6}{2}+c\,d^6\,x^7+\frac {d^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*} c^{7} x + \frac {7 c^{6} d x^{2}}{2} + 7 c^{5} d^{2} x^{3} + \frac {35 c^{4} d^{3} x^{4}}{4} + 7 c^{3} d^{4} x^{5} + \frac {7 c^{2} d^{5} x^{6}}{2} + c d^{6} x^{7} + \frac {d^{7} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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