Optimal. Leaf size=44 \[ \frac{1}{7} e^{7 x} x^3-\frac{3}{49} e^{7 x} x^2+\frac{6}{343} e^{7 x} x-\frac{6 e^{7 x}}{2401} \]
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Rubi [A] time = 0.0348359, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ \frac{1}{7} e^{7 x} x^3-\frac{3}{49} e^{7 x} x^2+\frac{6}{343} e^{7 x} x-\frac{6 e^{7 x}}{2401} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{7 x} x^3 \, dx &=\frac{1}{7} e^{7 x} x^3-\frac{3}{7} \int e^{7 x} x^2 \, dx\\ &=-\frac{3}{49} e^{7 x} x^2+\frac{1}{7} e^{7 x} x^3+\frac{6}{49} \int e^{7 x} x \, dx\\ &=\frac{6}{343} e^{7 x} x-\frac{3}{49} e^{7 x} x^2+\frac{1}{7} e^{7 x} x^3-\frac{6}{343} \int e^{7 x} \, dx\\ &=-\frac{6 e^{7 x}}{2401}+\frac{6}{343} e^{7 x} x-\frac{3}{49} e^{7 x} x^2+\frac{1}{7} e^{7 x} x^3\\ \end{align*}
Mathematica [A] time = 0.0073774, size = 24, normalized size = 0.55 \[ \frac{e^{7 x} \left (343 x^3-147 x^2+42 x-6\right )}{2401} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.021, size = 22, normalized size = 0.5 \begin{align*}{\frac{ \left ( 343\,{x}^{3}-147\,{x}^{2}+42\,x-6 \right ){{\rm e}^{7\,x}}}{2401}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964457, size = 28, normalized size = 0.64 \begin{align*} \frac{1}{2401} \,{\left (343 \, x^{3} - 147 \, x^{2} + 42 \, x - 6\right )} e^{\left (7 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.807989, size = 63, normalized size = 1.43 \begin{align*} \frac{1}{2401} \,{\left (343 \, x^{3} - 147 \, x^{2} + 42 \, x - 6\right )} e^{\left (7 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.088803, size = 20, normalized size = 0.45 \begin{align*} \frac{\left (343 x^{3} - 147 x^{2} + 42 x - 6\right ) e^{7 x}}{2401} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.40771, size = 28, normalized size = 0.64 \begin{align*} \frac{1}{2401} \,{\left (343 \, x^{3} - 147 \, x^{2} + 42 \, x - 6\right )} e^{\left (7 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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