Optimal. Leaf size=22 \[ x \left (x+\frac {\frac {e^{9 x}}{x}+x}{5 x^4}\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 6, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 14, 2197} \begin {gather*} \frac {e^{9 x}}{5 x^4}+x^2+\frac {1}{5 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-2 x^2+10 x^6+e^{9 x} (-4+9 x)}{x^5} \, dx\\ &=\frac {1}{5} \int \left (\frac {e^{9 x} (-4+9 x)}{x^5}+\frac {2 \left (-1+5 x^4\right )}{x^3}\right ) \, dx\\ &=\frac {1}{5} \int \frac {e^{9 x} (-4+9 x)}{x^5} \, dx+\frac {2}{5} \int \frac {-1+5 x^4}{x^3} \, dx\\ &=\frac {e^{9 x}}{5 x^4}+\frac {2}{5} \int \left (-\frac {1}{x^3}+5 x\right ) \, dx\\ &=\frac {e^{9 x}}{5 x^4}+\frac {1}{5 x^2}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.05 \begin {gather*} \frac {e^{9 x}}{5 x^4}+\frac {1}{5 x^2}+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 18, normalized size = 0.82 \begin {gather*} \frac {5 \, x^{6} + x^{2} + e^{\left (9 \, x\right )}}{5 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 18, normalized size = 0.82 \begin {gather*} \frac {5 \, x^{6} + x^{2} + e^{\left (9 \, x\right )}}{5 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 19, normalized size = 0.86
method | result | size |
derivativedivides | \(x^{2}+\frac {1}{5 x^{2}}+\frac {{\mathrm e}^{9 x}}{5 x^{4}}\) | \(19\) |
default | \(x^{2}+\frac {1}{5 x^{2}}+\frac {{\mathrm e}^{9 x}}{5 x^{4}}\) | \(19\) |
risch | \(x^{2}+\frac {1}{5 x^{2}}+\frac {{\mathrm e}^{9 x}}{5 x^{4}}\) | \(19\) |
norman | \(\frac {x^{6}+\frac {x^{2}}{5}+\frac {{\mathrm e}^{9 x}}{5}}{x^{4}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 23, normalized size = 1.05 \begin {gather*} x^{2} + \frac {1}{5 \, x^{2}} + \frac {6561}{5} \, \Gamma \left (-3, -9 \, x\right ) + \frac {26244}{5} \, \Gamma \left (-4, -9 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 20, normalized size = 0.91 \begin {gather*} \frac {\frac {{\mathrm {e}}^{9\,x}}{5}+\frac {x^2}{5}}{x^4}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 19, normalized size = 0.86 \begin {gather*} x^{2} + \frac {1}{5 x^{2}} + \frac {e^{9 x}}{5 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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