Optimal. Leaf size=39 \[ \frac {3}{20 \left (2 x^5+3\right )}-\frac {9}{80 \left (2 x^5+3\right )^2}+\frac {1}{40} \log \left (2 x^5+3\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {3}{20 \left (2 x^5+3\right )}-\frac {9}{80 \left (2 x^5+3\right )^2}+\frac {1}{40} \log \left (2 x^5+3\right ) \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {x^{14}}{\left (3+2 x^5\right )^3} \, dx &=\frac {1}{5} \operatorname {Subst}\left (\int \frac {x^2}{(3+2 x)^3} \, dx,x,x^5\right )\\ &=\frac {1}{5} \operatorname {Subst}\left (\int \left (\frac {9}{4 (3+2 x)^3}-\frac {3}{2 (3+2 x)^2}+\frac {1}{4 (3+2 x)}\right ) \, dx,x,x^5\right )\\ &=-\frac {9}{80 \left (3+2 x^5\right )^2}+\frac {3}{20 \left (3+2 x^5\right )}+\frac {1}{40} \log \left (3+2 x^5\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 0.85 \[ \frac {1}{80} \left (\frac {3 \left (8 x^5+9\right )}{\left (2 x^5+3\right )^2}+2 \log \left (2 x^5+3\right )\right ) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 33, normalized size = 0.85 \[ \frac {3 \left (8 x^5+9\right )}{80 \left (2 x^5+3\right )^2}+\frac {1}{40} \log \left (2 x^5+3\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 45, normalized size = 1.15 \[ \frac {24 \, x^{5} + 2 \, {\left (4 \, x^{10} + 12 \, x^{5} + 9\right )} \log \left (2 \, x^{5} + 3\right ) + 27}{80 \, {\left (4 \, x^{10} + 12 \, x^{5} + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 30, normalized size = 0.77 \[ -\frac {3 \, {\left (x^{10} + x^{5}\right )}}{20 \, {\left (2 \, x^{5} + 3\right )}^{2}} + \frac {1}{40} \, \log \left ({\left | 2 \, x^{5} + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 29, normalized size = 0.74
method | result | size |
norman | \(\frac {\frac {3 x^{5}}{10}+\frac {27}{80}}{\left (2 x^{5}+3\right )^{2}}+\frac {\ln \left (2 x^{5}+3\right )}{40}\) | \(29\) |
risch | \(\frac {\frac {3 x^{5}}{10}+\frac {27}{80}}{\left (2 x^{5}+3\right )^{2}}+\frac {\ln \left (2 x^{5}+3\right )}{40}\) | \(30\) |
meijerg | \(-\frac {x^{5} \left (6 x^{5}+6\right )}{360 \left (1+\frac {2 x^{5}}{3}\right )^{2}}+\frac {\ln \left (1+\frac {2 x^{5}}{3}\right )}{40}\) | \(33\) |
default | \(-\frac {9}{80 \left (2 x^{5}+3\right )^{2}}+\frac {3}{20 \left (2 x^{5}+3\right )}+\frac {\ln \left (2 x^{5}+3\right )}{40}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 34, normalized size = 0.87 \[ \frac {3 \, {\left (8 \, x^{5} + 9\right )}}{80 \, {\left (4 \, x^{10} + 12 \, x^{5} + 9\right )}} + \frac {1}{40} \, \log \left (2 \, x^{5} + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 29, normalized size = 0.74 \[ \frac {\ln \left (x^5+\frac {3}{2}\right )}{40}+\frac {\frac {3\,x^5}{40}+\frac {27}{320}}{x^{10}+3\,x^5+\frac {9}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 27, normalized size = 0.69 \[ \frac {24 x^{5} + 27}{320 x^{10} + 960 x^{5} + 720} + \frac {\log {\left (2 x^{5} + 3 \right )}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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