Optimal. Leaf size=50 \[ a^2 c x+\frac {1}{4} a (2 b c+a d) x^4+\frac {1}{7} b (b c+2 a d) x^7+\frac {1}{10} b^2 d x^{10} \]
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Rubi [A]
time = 0.02, antiderivative size = 50, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {380}
\begin {gather*} a^2 c x+\frac {1}{7} b x^7 (2 a d+b c)+\frac {1}{4} a x^4 (a d+2 b c)+\frac {1}{10} b^2 d x^{10} \end {gather*}
Antiderivative was successfully verified.
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Rule 380
Rubi steps
\begin {align*} \int \left (a+b x^3\right )^2 \left (c+d x^3\right ) \, dx &=\int \left (a^2 c+a (2 b c+a d) x^3+b (b c+2 a d) x^6+b^2 d x^9\right ) \, dx\\ &=a^2 c x+\frac {1}{4} a (2 b c+a d) x^4+\frac {1}{7} b (b c+2 a d) x^7+\frac {1}{10} b^2 d x^{10}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 50, normalized size = 1.00 \begin {gather*} a^2 c x+\frac {1}{4} a (2 b c+a d) x^4+\frac {1}{7} b (b c+2 a d) x^7+\frac {1}{10} b^2 d x^{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 49, normalized size = 0.98
method | result | size |
default | \(\frac {b^{2} d \,x^{10}}{10}+\frac {\left (2 a b d +b^{2} c \right ) x^{7}}{7}+\frac {\left (a^{2} d +2 a b c \right ) x^{4}}{4}+a^{2} c x\) | \(49\) |
norman | \(\frac {b^{2} d \,x^{10}}{10}+\left (\frac {2}{7} a b d +\frac {1}{7} b^{2} c \right ) x^{7}+\left (\frac {1}{4} a^{2} d +\frac {1}{2} a b c \right ) x^{4}+a^{2} c x\) | \(49\) |
gosper | \(\frac {1}{10} b^{2} d \,x^{10}+\frac {2}{7} x^{7} a b d +\frac {1}{7} x^{7} b^{2} c +\frac {1}{4} x^{4} a^{2} d +\frac {1}{2} x^{4} a b c +a^{2} c x\) | \(51\) |
risch | \(\frac {1}{10} b^{2} d \,x^{10}+\frac {2}{7} x^{7} a b d +\frac {1}{7} x^{7} b^{2} c +\frac {1}{4} x^{4} a^{2} d +\frac {1}{2} x^{4} a b c +a^{2} c x\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 48, normalized size = 0.96 \begin {gather*} \frac {1}{10} \, b^{2} d x^{10} + \frac {1}{7} \, {\left (b^{2} c + 2 \, a b d\right )} x^{7} + \frac {1}{4} \, {\left (2 \, a b c + a^{2} d\right )} x^{4} + a^{2} c x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.78, size = 48, normalized size = 0.96 \begin {gather*} \frac {1}{10} \, b^{2} d x^{10} + \frac {1}{7} \, {\left (b^{2} c + 2 \, a b d\right )} x^{7} + \frac {1}{4} \, {\left (2 \, a b c + a^{2} d\right )} x^{4} + a^{2} c x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 51, normalized size = 1.02 \begin {gather*} a^{2} c x + \frac {b^{2} d x^{10}}{10} + x^{7} \cdot \left (\frac {2 a b d}{7} + \frac {b^{2} c}{7}\right ) + x^{4} \left (\frac {a^{2} d}{4} + \frac {a b c}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.66, size = 50, normalized size = 1.00 \begin {gather*} \frac {1}{10} \, b^{2} d x^{10} + \frac {1}{7} \, b^{2} c x^{7} + \frac {2}{7} \, a b d x^{7} + \frac {1}{2} \, a b c x^{4} + \frac {1}{4} \, a^{2} d x^{4} + a^{2} c x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 48, normalized size = 0.96 \begin {gather*} x^4\,\left (\frac {d\,a^2}{4}+\frac {b\,c\,a}{2}\right )+x^7\,\left (\frac {c\,b^2}{7}+\frac {2\,a\,d\,b}{7}\right )+\frac {b^2\,d\,x^{10}}{10}+a^2\,c\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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