Optimal. Leaf size=30 \[ \frac {a^2 x^5}{5}+\frac {1}{3} a b x^6+\frac {b^2 x^7}{7} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {1607, 45}
\begin {gather*} \frac {a^2 x^5}{5}+\frac {1}{3} a b x^6+\frac {b^2 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 1607
Rubi steps
\begin {align*} \int \left (a x^2+b x^3\right )^2 \, dx &=\int x^4 (a+b x)^2 \, dx\\ &=\int \left (a^2 x^4+2 a b x^5+b^2 x^6\right ) \, dx\\ &=\frac {a^2 x^5}{5}+\frac {1}{3} a b x^6+\frac {b^2 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^5}{5}+\frac {1}{3} a b x^6+\frac {b^2 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {x^{5} \left (15 b^{2} x^{2}+35 a b x +21 a^{2}\right )}{105}\) | \(25\) |
default | \(\frac {1}{5} a^{2} x^{5}+\frac {1}{3} a b \,x^{6}+\frac {1}{7} b^{2} x^{7}\) | \(25\) |
norman | \(\frac {1}{5} a^{2} x^{5}+\frac {1}{3} a b \,x^{6}+\frac {1}{7} b^{2} x^{7}\) | \(25\) |
risch | \(\frac {1}{5} a^{2} x^{5}+\frac {1}{3} a b \,x^{6}+\frac {1}{7} b^{2} x^{7}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} \, b^{2} x^{7} + \frac {1}{3} \, a b x^{6} + \frac {1}{5} \, a^{2} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.32, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} \, b^{2} x^{7} + \frac {1}{3} \, a b x^{6} + \frac {1}{5} \, a^{2} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^{2} x^{5}}{5} + \frac {a b x^{6}}{3} + \frac {b^{2} x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.42, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} \, b^{2} x^{7} + \frac {1}{3} \, a b x^{6} + \frac {1}{5} \, a^{2} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^5}{5}+\frac {a\,b\,x^6}{3}+\frac {b^2\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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