Optimal. Leaf size=23 \[ \frac {\left (a+b x+c x^2+d x^3\right )^{p+1}}{x^3} \]
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Rubi [A] time = 0.04, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {1590} \[ \frac {\left (a+b x+c x^2+d x^3\right )^{p+1}}{x^3} \]
Antiderivative was successfully verified.
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Rule 1590
Rubi steps
\begin {align*} \int \frac {\left (a+b x+c x^2+d x^3\right )^p \left (-3 a+b (-2+p) x+c (-1+2 p) x^2+3 d p x^3\right )}{x^4} \, dx &=\frac {\left (a+b x+c x^2+d x^3\right )^{1+p}}{x^3}\\ \end {align*}
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Mathematica [A] time = 0.19, size = 21, normalized size = 0.91 \[ \frac {(a+x (b+x (c+d x)))^{p+1}}{x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 36, normalized size = 1.57 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (3 \, d p x^{3} + c {\left (2 \, p - 1\right )} x^{2} + b {\left (p - 2\right )} x - 3 \, a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 24, normalized size = 1.04 \[ \frac {\left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 36, normalized size = 1.57 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.35, size = 23, normalized size = 1.00 \[ \frac {{\left (d\,x^3+c\,x^2+b\,x+a\right )}^{p+1}}{x^3} \]
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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