Optimal. Leaf size=19 \[ \frac{\left (a+b x^n\right )^{17}}{17 b n} \]
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Rubi [A] time = 0.0044505, antiderivative size = 19, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0066572, size = 19, normalized size = 1. \[ \frac{\left (a+b x^n\right )^{17}}{17 b n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.031, size = 260, normalized size = 13.7 \begin{align*}{\frac{{b}^{16} \left ({x}^{n} \right ) ^{17}}{17\,n}}+{\frac{{b}^{15}a \left ({x}^{n} \right ) ^{16}}{n}}+8\,{\frac{{a}^{2}{b}^{14} \left ({x}^{n} \right ) ^{15}}{n}}+40\,{\frac{{a}^{3}{b}^{13} \left ({x}^{n} \right ) ^{14}}{n}}+140\,{\frac{{a}^{4}{b}^{12} \left ({x}^{n} \right ) ^{13}}{n}}+364\,{\frac{{a}^{5}{b}^{11} \left ({x}^{n} \right ) ^{12}}{n}}+728\,{\frac{{a}^{6}{b}^{10} \left ({x}^{n} \right ) ^{11}}{n}}+1144\,{\frac{{b}^{9}{a}^{7} \left ({x}^{n} \right ) ^{10}}{n}}+1430\,{\frac{{a}^{8}{b}^{8} \left ({x}^{n} \right ) ^{9}}{n}}+1430\,{\frac{{a}^{9}{b}^{7} \left ({x}^{n} \right ) ^{8}}{n}}+1144\,{\frac{{a}^{10}{b}^{6} \left ({x}^{n} \right ) ^{7}}{n}}+728\,{\frac{{a}^{11}{b}^{5} \left ({x}^{n} \right ) ^{6}}{n}}+364\,{\frac{{a}^{12}{b}^{4} \left ({x}^{n} \right ) ^{5}}{n}}+140\,{\frac{{a}^{13}{b}^{3} \left ({x}^{n} \right ) ^{4}}{n}}+40\,{\frac{{a}^{14}{b}^{2} \left ({x}^{n} \right ) ^{3}}{n}}+8\,{\frac{{a}^{15}b \left ({x}^{n} \right ) ^{2}}{n}}+{\frac{{a}^{16}{x}^{n}}{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.971877, size = 23, normalized size = 1.21 \begin{align*} \frac{{\left (b x^{n} + a\right )}^{17}}{17 \, b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.09755, size = 537, normalized size = 28.26 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.21411, size = 289, normalized size = 15.21 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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