Optimal. Leaf size=17 \[ \frac {(a+b x)^4}{4 b c^2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {21, 32} \[ \frac {(a+b x)^4}{4 b c^2} \]
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{(a c+b c x)^2} \, dx &=\frac {\int (a+b x)^3 \, dx}{c^2}\\ &=\frac {(a+b x)^4}{4 b c^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {(a+b x)^4}{4 b c^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 37, normalized size = 2.18 \[ \frac {b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a^{3} x}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 18, normalized size = 1.06 \[ \frac {{\left (b c x + a c\right )}^{4}}{4 \, b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {\left (b x +a \right )^{4}}{4 b \,c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.31, size = 37, normalized size = 2.18 \[ \frac {b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a^{3} x}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 43, normalized size = 2.53 \[ \frac {a^3\,x}{c^2}+\frac {b^3\,x^4}{4\,c^2}+\frac {3\,a^2\,b\,x^2}{2\,c^2}+\frac {a\,b^2\,x^3}{c^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 46, normalized size = 2.71 \[ \frac {a^{3} x}{c^{2}} + \frac {3 a^{2} b x^{2}}{2 c^{2}} + \frac {a b^{2} x^{3}}{c^{2}} + \frac {b^{3} x^{4}}{4 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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