Optimal. Leaf size=24 \[ \frac {\left (b x+c x^2+d x^3\right )^{n+1}}{n+1} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {1588} \[ \frac {\left (b x+c x^2+d x^3\right )^{n+1}}{n+1} \]
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 (b x+c x^2+d x^3\right )^n \, dx &=\frac {\left (b x+c x^2+d x^3\right )^{1+n}}{1+n}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 21, normalized size = 0.88 \[ \frac {(x (b+x (c+d x)))^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 36, normalized size = 1.50 \[ \frac {{\left (d x^{3} + c x^{2} + b x\right )} {\left (d x^{3} + c x^{2} + b x\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 24, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + b x\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 34, normalized size = 1.42 \[ \frac {\left (d \,x^{2}+c x +b \right ) x \left (d \,x^{3}+c \,x^{2}+b x \right )^{n}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 24, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + b x\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.12, size = 46, normalized size = 1.92 \[ \left (\frac {b\,x}{n+1}+\frac {c\,x^2}{n+1}+\frac {d\,x^3}{n+1}\right )\,{\left (d\,x^3+c\,x^2+b\,x\right )}^n \]
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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