Optimal. Leaf size=20 \[ \frac{\left (a+b x+d x^3\right )^{n+1}}{n+1} \]
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Rubi [A] time = 0.0099577, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1588} \[ \frac{\left (a+b x+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \left (b+3 d x^2\right ) \left (a+b x+d x^3\right )^n \, dx &=\frac{\left (a+b x+d x^3\right )^{1+n}}{1+n}\\ \end{align*}
Mathematica [A] time = 0.0085864, size = 20, normalized size = 1. \[ \frac{\left (a+b x+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 21, normalized size = 1.1 \begin{align*}{\frac{ \left ( d{x}^{3}+bx+a \right ) ^{1+n}}{1+n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46924, size = 63, normalized size = 3.15 \begin{align*} \frac{{\left (d x^{3} + b x + a\right )}{\left (d x^{3} + b x + a\right )}^{n}}{n + 1} \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 = 1.18805, size = 72, normalized size = 3.6 \begin{align*} \frac{{\left (d x^{3} + b x + a\right )}^{n} d x^{3} +{\left (d x^{3} + b x + a\right )}^{n} b x +{\left (d x^{3} + b x + a\right )}^{n} a}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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