Optimal. Leaf size=15 \[ \frac {c (a+b x)^7}{7 b} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {21, 32} \[ \frac {c (a+b x)^7}{7 b} \]
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int (a+b x)^5 (a c+b c x) \, dx &=c \int (a+b x)^6 \, dx\\ &=\frac {c (a+b x)^7}{7 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {c (a+b x)^7}{7 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 71, normalized size = 4.73 \[ \frac {1}{7} x^{7} c b^{6} + x^{6} c b^{5} a + 3 x^{5} c b^{4} a^{2} + 5 x^{4} c b^{3} a^{3} + 5 x^{3} c b^{2} a^{4} + 3 x^{2} c b a^{5} + x c a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.09, size = 71, normalized size = 4.73 \[ \frac {1}{7} \, b^{6} c x^{7} + a b^{5} c x^{6} + 3 \, a^{2} b^{4} c x^{5} + 5 \, a^{3} b^{3} c x^{4} + 5 \, a^{4} b^{2} c x^{3} + 3 \, a^{5} b c x^{2} + a^{6} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 72, normalized size = 4.80 \[ \frac {1}{7} b^{6} c \,x^{7}+a \,b^{5} c \,x^{6}+3 a^{2} b^{4} c \,x^{5}+5 a^{3} b^{3} c \,x^{4}+5 a^{4} b^{2} c \,x^{3}+3 a^{5} b c \,x^{2}+a^{6} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.35, size = 71, normalized size = 4.73 \[ \frac {1}{7} \, b^{6} c x^{7} + a b^{5} c x^{6} + 3 \, a^{2} b^{4} c x^{5} + 5 \, a^{3} b^{3} c x^{4} + 5 \, a^{4} b^{2} c x^{3} + 3 \, a^{5} b c x^{2} + a^{6} c x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 71, normalized size = 4.73 \[ c\,a^6\,x+3\,c\,a^5\,b\,x^2+5\,c\,a^4\,b^2\,x^3+5\,c\,a^3\,b^3\,x^4+3\,c\,a^2\,b^4\,x^5+c\,a\,b^5\,x^6+\frac {c\,b^6\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 78, normalized size = 5.20 \[ a^{6} c x + 3 a^{5} b c x^{2} + 5 a^{4} b^{2} c x^{3} + 5 a^{3} b^{3} c x^{4} + 3 a^{2} b^{4} c x^{5} + a b^{5} c x^{6} + \frac {b^{6} c x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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