Optimal. Leaf size=19 \[ \frac {\left (a+b x^n\right )^{17}}{17 b n} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {261} \[ \frac {\left (a+b x^n\right )^{17}}{17 b n} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^{-1+n} \left (a+b x^n\right )^{16} \, dx &=\frac {\left (a+b x^n\right )^{17}}{17 b n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \[ \frac {\left (a+b x^n\right )^{17}}{17 b n} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 214, normalized size = 11.26 \[ \frac {b^{16} x^{17 \, n} + 17 \, a b^{15} x^{16 \, n} + 136 \, a^{2} b^{14} x^{15 \, n} + 680 \, a^{3} b^{13} x^{14 \, n} + 2380 \, a^{4} b^{12} x^{13 \, n} + 6188 \, a^{5} b^{11} x^{12 \, n} + 12376 \, a^{6} b^{10} x^{11 \, n} + 19448 \, a^{7} b^{9} x^{10 \, n} + 24310 \, a^{8} b^{8} x^{9 \, n} + 24310 \, a^{9} b^{7} x^{8 \, n} + 19448 \, a^{10} b^{6} x^{7 \, n} + 12376 \, a^{11} b^{5} x^{6 \, n} + 6188 \, a^{12} b^{4} x^{5 \, n} + 2380 \, a^{13} b^{3} x^{4 \, n} + 680 \, a^{14} b^{2} x^{3 \, n} + 136 \, a^{15} b x^{2 \, n} + 17 \, a^{16} x^{n}}{17 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 214, normalized size = 11.26 \[ \frac {b^{16} x^{17 \, n} + 17 \, a b^{15} x^{16 \, n} + 136 \, a^{2} b^{14} x^{15 \, n} + 680 \, a^{3} b^{13} x^{14 \, n} + 2380 \, a^{4} b^{12} x^{13 \, n} + 6188 \, a^{5} b^{11} x^{12 \, n} + 12376 \, a^{6} b^{10} x^{11 \, n} + 19448 \, a^{7} b^{9} x^{10 \, n} + 24310 \, a^{8} b^{8} x^{9 \, n} + 24310 \, a^{9} b^{7} x^{8 \, n} + 19448 \, a^{10} b^{6} x^{7 \, n} + 12376 \, a^{11} b^{5} x^{6 \, n} + 6188 \, a^{12} b^{4} x^{5 \, n} + 2380 \, a^{13} b^{3} x^{4 \, n} + 680 \, a^{14} b^{2} x^{3 \, n} + 136 \, a^{15} b x^{2 \, n} + 17 \, a^{16} x^{n}}{17 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 260, normalized size = 13.68 \[ \frac {a^{16} x^{n}}{n}+\frac {8 a^{15} b \,x^{2 n}}{n}+\frac {40 a^{14} b^{2} x^{3 n}}{n}+\frac {140 a^{13} b^{3} x^{4 n}}{n}+\frac {364 a^{12} b^{4} x^{5 n}}{n}+\frac {728 a^{11} b^{5} x^{6 n}}{n}+\frac {1144 a^{10} b^{6} x^{7 n}}{n}+\frac {1430 a^{9} b^{7} x^{8 n}}{n}+\frac {1430 a^{8} b^{8} x^{9 n}}{n}+\frac {1144 a^{7} b^{9} x^{10 n}}{n}+\frac {728 a^{6} b^{10} x^{11 n}}{n}+\frac {364 a^{5} b^{11} x^{12 n}}{n}+\frac {140 a^{4} b^{12} x^{13 n}}{n}+\frac {40 a^{3} b^{13} x^{14 n}}{n}+\frac {8 a^{2} b^{14} x^{15 n}}{n}+\frac {a \,b^{15} x^{16 n}}{n}+\frac {b^{16} x^{17 n}}{17 n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 17, normalized size = 0.89 \[ \frac {{\left (b x^{n} + a\right )}^{17}}{17 \, b n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.87, size = 259, normalized size = 13.63 \[ \frac {a^{16}\,x^n}{n}+\frac {b^{16}\,x^{17\,n}}{17\,n}+\frac {40\,a^{14}\,b^2\,x^{3\,n}}{n}+\frac {140\,a^{13}\,b^3\,x^{4\,n}}{n}+\frac {364\,a^{12}\,b^4\,x^{5\,n}}{n}+\frac {728\,a^{11}\,b^5\,x^{6\,n}}{n}+\frac {1144\,a^{10}\,b^6\,x^{7\,n}}{n}+\frac {1430\,a^9\,b^7\,x^{8\,n}}{n}+\frac {1430\,a^8\,b^8\,x^{9\,n}}{n}+\frac {1144\,a^7\,b^9\,x^{10\,n}}{n}+\frac {728\,a^6\,b^{10}\,x^{11\,n}}{n}+\frac {364\,a^5\,b^{11}\,x^{12\,n}}{n}+\frac {140\,a^4\,b^{12}\,x^{13\,n}}{n}+\frac {40\,a^3\,b^{13}\,x^{14\,n}}{n}+\frac {8\,a^2\,b^{14}\,x^{15\,n}}{n}+\frac {8\,a^{15}\,b\,x^{2\,n}}{n}+\frac {a\,b^{15}\,x^{16\,n}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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