Optimal. Leaf size=25 \[ \frac {\left (a+b x+c x^2+d x^3\right )^{n+1}}{n+1} \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {1588} \[ \frac {\left (a+b x+c x^2+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \left (b+2 c x+3 d x^2\right ) \left (a+b x+c x^2+d x^3\right )^n \, dx &=\frac {\left (a+b x+c x^2+d x^3\right )^{1+n}}{1+n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.92 \[ \frac {(a+x (b+x (c+d x)))^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 38, normalized size = 1.52 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 25, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 1.04 \[ \frac {\left (d \,x^{3}+c \,x^{2}+b x +a \right )^{n +1}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 25, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.19, size = 54, normalized size = 2.16 \[ {\left (d\,x^3+c\,x^2+b\,x+a\right )}^n\,\left (\frac {a}{n+1}+\frac {b\,x}{n+1}+\frac {c\,x^2}{n+1}+\frac {d\,x^3}{n+1}\right ) \]
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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