Optimal. Leaf size=14 \[ \frac {(c+d x)^{11}}{11 d} \]
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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} \[ \frac {(c+d x)^{11}}{11 d} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (c+d x)^{10} \, dx &=\frac {(c+d x)^{11}}{11 d}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {(c+d x)^{11}}{11 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.36, size = 108, normalized size = 7.71 \[ \frac {1}{11} x^{11} d^{10} + x^{10} d^{9} c + 5 x^{9} d^{8} c^{2} + 15 x^{8} d^{7} c^{3} + 30 x^{7} d^{6} c^{4} + 42 x^{6} d^{5} c^{5} + 42 x^{5} d^{4} c^{6} + 30 x^{4} d^{3} c^{7} + 15 x^{3} d^{2} c^{8} + 5 x^{2} d c^{9} + x c^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.28, size = 12, normalized size = 0.86 \[ \frac {{\left (d x + c\right )}^{11}}{11 \, d} \]
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 \[ \frac {\left (d x +c \right )^{11}}{11 d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 12, normalized size = 0.86 \[ \frac {{\left (d x + c\right )}^{11}}{11 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 108, normalized size = 7.71 \[ c^{10}\,x+5\,c^9\,d\,x^2+15\,c^8\,d^2\,x^3+30\,c^7\,d^3\,x^4+42\,c^6\,d^4\,x^5+42\,c^5\,d^5\,x^6+30\,c^4\,d^6\,x^7+15\,c^3\,d^7\,x^8+5\,c^2\,d^8\,x^9+c\,d^9\,x^{10}+\frac {d^{10}\,x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 114, normalized size = 8.14 \[ c^{10} x + 5 c^{9} d x^{2} + 15 c^{8} d^{2} x^{3} + 30 c^{7} d^{3} x^{4} + 42 c^{6} d^{4} x^{5} + 42 c^{5} d^{5} x^{6} + 30 c^{4} d^{6} x^{7} + 15 c^{3} d^{7} x^{8} + 5 c^{2} d^{8} x^{9} + c d^{9} x^{10} + \frac {d^{10} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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