Optimal. Leaf size=16 \[ \frac {x \left (d x^3\right )^n}{3 n+1} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {15, 30} \[ \frac {x \left (d x^3\right )^n}{3 n+1} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (d x^3\right )^n \, dx &=\left (x^{-3 n} \left (d x^3\right )^n\right ) \int x^{3 n} \, dx\\ &=\frac {x \left (d x^3\right )^n}{1+3 n}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {x \left (d x^3\right )^n}{3 n+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 16, normalized size = 1.00 \[ \frac {\left (d x^{3}\right )^{n} x}{3 \, n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 16, normalized size = 1.00 \[ \frac {\left (d x^{3}\right )^{n} x}{3 \, n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 1.06 \[ \frac {x \left (d \,x^{3}\right )^{n}}{3 n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 17, normalized size = 1.06 \[ \frac {d^{n} x x^{3 \, n}}{3 \, n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.50, size = 16, normalized size = 1.00 \[ \frac {x\,{\left (d\,x^3\right )}^n}{3\,n+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \begin {cases} \frac {d^{n} x \left (x^{3}\right )^{n}}{3 n + 1} & \text {for}\: n \neq - \frac {1}{3} \\\int \frac {1}{\sqrt [3]{d x^{3}}}\, dx & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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