Optimal. Leaf size=14 \[ \frac{(a+b x)^5}{5 b} \]
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Rubi [A] time = 0.0023447, antiderivative size = 14, normalized size of antiderivative = 1., 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 = {27, 32} \[ \frac{(a+b x)^5}{5 b} \]
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin{align*} \int \left (a^2+2 a b x+b^2 x^2\right )^2 \, dx &=\int (a+b x)^4 \, dx\\ &=\frac{(a+b x)^5}{5 b}\\ \end{align*}
Mathematica [A] time = 0.001292, size = 14, normalized size = 1. \[ \frac{(a+b x)^5}{5 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.039, size = 43, normalized size = 3.1 \begin{align*}{\frac{{b}^{4}{x}^{5}}{5}}+a{b}^{3}{x}^{4}+2\,{b}^{2}{a}^{2}{x}^{3}+2\,{a}^{3}b{x}^{2}+{a}^{4}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.16626, size = 72, normalized size = 5.14 \begin{align*} \frac{1}{5} \, b^{4} x^{5} + a b^{3} x^{4} + \frac{4}{3} \, a^{2} b^{2} x^{3} + a^{4} x + \frac{2}{3} \,{\left (b^{2} x^{3} + 3 \, a b x^{2}\right )} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.39525, size = 85, normalized size = 6.07 \begin{align*} \frac{1}{5} x^{5} b^{4} + x^{4} b^{3} a + 2 x^{3} b^{2} a^{2} + 2 x^{2} b a^{3} + x a^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.065736, size = 42, normalized size = 3. \begin{align*} a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.14409, size = 57, normalized size = 4.07 \begin{align*} \frac{1}{5} \, b^{4} x^{5} + a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{3} + 2 \, a^{3} b x^{2} + a^{4} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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