Optimal. Leaf size=21 \[ -\frac{\left (a+b \sqrt{x}\right )^6}{3 a x^3} \]
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Rubi [A] time = 0.0032821, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\left (a+b \sqrt{x}\right )^6}{3 a x^3} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt{x}\right )^5}{x^4} \, dx &=-\frac{\left (a+b \sqrt{x}\right )^6}{3 a x^3}\\ \end{align*}
Mathematica [A] time = 0.0046224, size = 21, normalized size = 1. \[ -\frac{\left (a+b \sqrt{x}\right )^6}{3 a x^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 58, normalized size = 2.8 \begin{align*} -2\,{\frac{{b}^{5}}{\sqrt{x}}}-5\,{\frac{a{b}^{4}}{x}}-{\frac{20\,{a}^{2}{b}^{3}}{3}{x}^{-{\frac{3}{2}}}}-5\,{\frac{{a}^{3}{b}^{2}}{{x}^{2}}}-2\,{\frac{{a}^{4}b}{{x}^{5/2}}}-{\frac{{a}^{5}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.51152, size = 74, normalized size = 3.52 \begin{align*} -\frac{6 \, b^{5} x^{\frac{5}{2}} + 15 \, a b^{4} x^{2} + 20 \, a^{2} b^{3} x^{\frac{3}{2}} + 15 \, a^{3} b^{2} x + 6 \, a^{4} b \sqrt{x} + a^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.49889, size = 128, normalized size = 6.1 \begin{align*} -\frac{15 \, a b^{4} x^{2} + 15 \, a^{3} b^{2} x + a^{5} + 2 \,{\left (3 \, b^{5} x^{2} + 10 \, a^{2} b^{3} x + 3 \, a^{4} b\right )} \sqrt{x}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.27584, size = 66, normalized size = 3.14 \begin{align*} - \frac{a^{5}}{3 x^{3}} - \frac{2 a^{4} b}{x^{\frac{5}{2}}} - \frac{5 a^{3} b^{2}}{x^{2}} - \frac{20 a^{2} b^{3}}{3 x^{\frac{3}{2}}} - \frac{5 a b^{4}}{x} - \frac{2 b^{5}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.09051, size = 74, normalized size = 3.52 \begin{align*} -\frac{6 \, b^{5} x^{\frac{5}{2}} + 15 \, a b^{4} x^{2} + 20 \, a^{2} b^{3} x^{\frac{3}{2}} + 15 \, a^{3} b^{2} x + 6 \, a^{4} b \sqrt{x} + a^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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