Optimal. Leaf size=27 \[ \frac {\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1593, 261} \[ \frac {\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
Antiderivative was successfully verified.
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Rule 261
Rule 1593
Rubi steps
\begin {align*} \int \left (a x^m+b x^{1+6 m}\right )^5 \, dx &=\int x^{5 m} \left (a+b x^{1+5 m}\right )^5 \, dx\\ &=\frac {\left (a+b x^{1+5 m}\right )^6}{6 b (1+5 m)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \[ \frac {\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 93, normalized size = 3.44 \[ \frac {b^{5} x^{6} x^{30 \, m} + 6 \, a b^{4} x^{5} x^{25 \, m} + 15 \, a^{2} b^{3} x^{4} x^{20 \, m} + 20 \, a^{3} b^{2} x^{3} x^{15 \, m} + 15 \, a^{4} b x^{2} x^{10 \, m} + 6 \, a^{5} x x^{5 \, m}}{6 \, {\left (5 \, m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 93, normalized size = 3.44 \[ \frac {b^{5} x^{6} x^{30 \, m} + 6 \, a b^{4} x^{5} x^{25 \, m} + 15 \, a^{2} b^{3} x^{4} x^{20 \, m} + 20 \, a^{3} b^{2} x^{3} x^{15 \, m} + 15 \, a^{4} b x^{2} x^{10 \, m} + 6 \, a^{5} x x^{5 \, m}}{6 \, {\left (5 \, m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 126, normalized size = 4.67 \[ \frac {b^{5} x^{6} x^{30 m}}{6+30 m}+\frac {a \,b^{4} x^{5} x^{25 m}}{5 m +1}+\frac {5 a^{2} b^{3} x^{4} x^{20 m}}{2 \left (5 m +1\right )}+\frac {10 a^{3} b^{2} x^{3} x^{15 m}}{3 \left (5 m +1\right )}+\frac {5 a^{4} b \,x^{2} x^{10 m}}{2 \left (5 m +1\right )}+\frac {a^{5} x \,x^{5 m}}{5 m +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.41, size = 121, normalized size = 4.48 \[ \frac {b^{5} x^{30 \, m + 6}}{6 \, {\left (5 \, m + 1\right )}} + \frac {a b^{4} x^{25 \, m + 5}}{5 \, m + 1} + \frac {5 \, a^{2} b^{3} x^{20 \, m + 4}}{2 \, {\left (5 \, m + 1\right )}} + \frac {10 \, a^{3} b^{2} x^{15 \, m + 3}}{3 \, {\left (5 \, m + 1\right )}} + \frac {5 \, a^{4} b x^{10 \, m + 2}}{2 \, {\left (5 \, m + 1\right )}} + \frac {a^{5} x^{5 \, m + 1}}{5 \, m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.44, size = 124, normalized size = 4.59 \[ \frac {b^5\,x^{30\,m}\,x^6}{30\,m+6}+\frac {a^5\,x\,x^{5\,m}}{5\,m+1}+\frac {5\,a^4\,b\,x^{10\,m}\,x^2}{10\,m+2}+\frac {a\,b^4\,x^{25\,m}\,x^5}{5\,m+1}+\frac {5\,a^2\,b^3\,x^{20\,m}\,x^4}{10\,m+2}+\frac {10\,a^3\,b^2\,x^{15\,m}\,x^3}{15\,m+3} \]
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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