Optimal. Leaf size=33 \[ \frac {1}{5} A b x^5+\frac {1}{7} (b B+A c) x^7+\frac {1}{9} B c x^9 \]
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Rubi [A]
time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1598, 459}
\begin {gather*} \frac {1}{7} x^7 (A c+b B)+\frac {1}{5} A b x^5+\frac {1}{9} B c x^9 \end {gather*}
Antiderivative was successfully verified.
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Rule 459
Rule 1598
Rubi steps
\begin {align*} \int x^2 \left (A+B x^2\right ) \left (b x^2+c x^4\right ) \, dx &=\int x^4 \left (A+B x^2\right ) \left (b+c x^2\right ) \, dx\\ &=\int \left (A b x^4+(b B+A c) x^6+B c x^8\right ) \, dx\\ &=\frac {1}{5} A b x^5+\frac {1}{7} (b B+A c) x^7+\frac {1}{9} B c x^9\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 33, normalized size = 1.00 \begin {gather*} \frac {1}{5} A b x^5+\frac {1}{7} (b B+A c) x^7+\frac {1}{9} B c x^9 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 28, normalized size = 0.85
method | result | size |
default | \(\frac {A b \,x^{5}}{5}+\frac {\left (A c +B b \right ) x^{7}}{7}+\frac {B c \,x^{9}}{9}\) | \(28\) |
norman | \(\frac {B c \,x^{9}}{9}+\left (\frac {A c}{7}+\frac {B b}{7}\right ) x^{7}+\frac {A b \,x^{5}}{5}\) | \(29\) |
risch | \(\frac {1}{5} A b \,x^{5}+\frac {1}{7} x^{7} A c +\frac {1}{7} b B \,x^{7}+\frac {1}{9} B c \,x^{9}\) | \(30\) |
gosper | \(\frac {x^{5} \left (35 B c \,x^{4}+45 A c \,x^{2}+45 b B \,x^{2}+63 A b \right )}{315}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{9} \, B c x^{9} + \frac {1}{7} \, {\left (B b + A c\right )} x^{7} + \frac {1}{5} \, A b x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.91, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{9} \, B c x^{9} + \frac {1}{7} \, {\left (B b + A c\right )} x^{7} + \frac {1}{5} \, A b x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 29, normalized size = 0.88 \begin {gather*} \frac {A b x^{5}}{5} + \frac {B c x^{9}}{9} + x^{7} \left (\frac {A c}{7} + \frac {B b}{7}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.46, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{9} \, B c x^{9} + \frac {1}{7} \, B b x^{7} + \frac {1}{7} \, A c x^{7} + \frac {1}{5} \, A b x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 28, normalized size = 0.85 \begin {gather*} \frac {B\,c\,x^9}{9}+\left (\frac {A\,c}{7}+\frac {B\,b}{7}\right )\,x^7+\frac {A\,b\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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