Optimal. Leaf size=28 \[ \frac {3+x+21 \left (-x-x^2\right )^2-x \log (x)}{5 x} \]
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Rubi [A]
time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.18, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {12, 14}
\begin {gather*} \frac {21 x^3}{5}+\frac {42 x^2}{5}+\frac {21 x}{5}+\frac {3}{5 x}-\frac {\log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-3-x+21 x^2+84 x^3+63 x^4}{x^2} \, dx\\ &=\frac {1}{5} \int \left (21-\frac {3}{x^2}-\frac {1}{x}+84 x+63 x^2\right ) \, dx\\ &=\frac {3}{5 x}+\frac {21 x}{5}+\frac {42 x^2}{5}+\frac {21 x^3}{5}-\frac {\log (x)}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 27, normalized size = 0.96 \begin {gather*} \frac {1}{5} \left (\frac {3}{x}+21 x+42 x^2+21 x^3-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 24, normalized size = 0.86
method | result | size |
default | \(\frac {21 x^{3}}{5}+\frac {42 x^{2}}{5}+\frac {21 x}{5}+\frac {3}{5 x}-\frac {\ln \left (x \right )}{5}\) | \(24\) |
risch | \(\frac {21 x^{3}}{5}+\frac {42 x^{2}}{5}+\frac {21 x}{5}+\frac {3}{5 x}-\frac {\ln \left (x \right )}{5}\) | \(24\) |
norman | \(\frac {\frac {3}{5}+\frac {21}{5} x^{2}+\frac {42}{5} x^{3}+\frac {21}{5} x^{4}}{x}-\frac {\ln \left (x \right )}{5}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 0.82 \begin {gather*} \frac {21}{5} \, x^{3} + \frac {42}{5} \, x^{2} + \frac {21}{5} \, x + \frac {3}{5 \, x} - \frac {1}{5} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 27, normalized size = 0.96 \begin {gather*} \frac {21 \, x^{4} + 42 \, x^{3} + 21 \, x^{2} - x \log \left (x\right ) + 3}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 27, normalized size = 0.96 \begin {gather*} \frac {21 x^{3}}{5} + \frac {42 x^{2}}{5} + \frac {21 x}{5} - \frac {\log {\left (x \right )}}{5} + \frac {3}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 24, normalized size = 0.86 \begin {gather*} \frac {21}{5} \, x^{3} + \frac {42}{5} \, x^{2} + \frac {21}{5} \, x + \frac {3}{5 \, x} - \frac {1}{5} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 23, normalized size = 0.82 \begin {gather*} \frac {21\,x}{5}-\frac {\ln \left (x\right )}{5}+\frac {3}{5\,x}+\frac {42\,x^2}{5}+\frac {21\,x^3}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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