Optimal. Leaf size=42 \[ a d x+\frac {1}{4} (b d+a e) x^4+\frac {1}{7} (c d+b e) x^7+\frac {1}{10} c e x^{10} \]
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Rubi [A]
time = 0.02, antiderivative size = 42, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1421}
\begin {gather*} \frac {1}{4} x^4 (a e+b d)+a d x+\frac {1}{7} x^7 (b e+c d)+\frac {1}{10} c e x^{10} \end {gather*}
Antiderivative was successfully verified.
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Rule 1421
Rubi steps
\begin {align*} \int \left (d+e x^3\right ) \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d+(b d+a e) x^3+(c d+b e) x^6+c e x^9\right ) \, dx\\ &=a d x+\frac {1}{4} (b d+a e) x^4+\frac {1}{7} (c d+b e) x^7+\frac {1}{10} c e x^{10}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 1.00 \begin {gather*} a d x+\frac {1}{4} (b d+a e) x^4+\frac {1}{7} (c d+b e) x^7+\frac {1}{10} c e x^{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 37, normalized size = 0.88
method | result | size |
default | \(a d x +\frac {\left (a e +b d \right ) x^{4}}{4}+\frac {\left (e b +c d \right ) x^{7}}{7}+\frac {c e \,x^{10}}{10}\) | \(37\) |
norman | \(\frac {c e \,x^{10}}{10}+\left (\frac {e b}{7}+\frac {c d}{7}\right ) x^{7}+\left (\frac {a e}{4}+\frac {b d}{4}\right ) x^{4}+a d x\) | \(39\) |
gosper | \(\frac {1}{10} c e \,x^{10}+\frac {1}{7} x^{7} e b +\frac {1}{7} x^{7} c d +\frac {1}{4} x^{4} a e +\frac {1}{4} x^{4} b d +a d x\) | \(41\) |
risch | \(\frac {1}{10} c e \,x^{10}+\frac {1}{7} x^{7} e b +\frac {1}{7} x^{7} c d +\frac {1}{4} x^{4} a e +\frac {1}{4} x^{4} b d +a d x\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 39, normalized size = 0.93 \begin {gather*} \frac {1}{10} \, c x^{10} e + \frac {1}{7} \, {\left (c d + b e\right )} x^{7} + \frac {1}{4} \, {\left (b d + a e\right )} x^{4} + a d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 42, normalized size = 1.00 \begin {gather*} \frac {1}{7} \, c d x^{7} + \frac {1}{4} \, b d x^{4} + a d x + \frac {1}{140} \, {\left (14 \, c x^{10} + 20 \, b x^{7} + 35 \, a x^{4}\right )} e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 39, normalized size = 0.93 \begin {gather*} a d x + \frac {c e x^{10}}{10} + x^{7} \left (\frac {b e}{7} + \frac {c d}{7}\right ) + x^{4} \left (\frac {a e}{4} + \frac {b d}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.08, size = 43, normalized size = 1.02 \begin {gather*} \frac {1}{10} \, c x^{10} e + \frac {1}{7} \, c d x^{7} + \frac {1}{7} \, b x^{7} e + \frac {1}{4} \, b d x^{4} + \frac {1}{4} \, a x^{4} e + a d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 38, normalized size = 0.90 \begin {gather*} \frac {c\,e\,x^{10}}{10}+\left (\frac {b\,e}{7}+\frac {c\,d}{7}\right )\,x^7+\left (\frac {a\,e}{4}+\frac {b\,d}{4}\right )\,x^4+a\,d\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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