Optimal. Leaf size=16 \[ \frac {(b x)^{n+1}}{b (n+1)} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {32} \[ \frac {(b x)^{n+1}}{b (n+1)} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (b x)^n \, dx &=\frac {(b x)^{1+n}}{b (1+n)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.75 \[ \frac {x (b x)^n}{n+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 12, normalized size = 0.75 \[ \frac {\left (b x\right )^{n} x}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 16, normalized size = 1.00 \[ \frac {\left (b x\right )^{n + 1}}{b {\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {x \left (b x \right )^{n}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 16, normalized size = 1.00 \[ \frac {\left (b x\right )^{n + 1}}{b {\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 12, normalized size = 0.75 \[ \frac {x\,{\left (b\,x\right )}^n}{n+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 1.06 \[ \frac {\begin {cases} \frac {\left (b x\right )^{n + 1}}{n + 1} & \text {for}\: n \neq -1 \\\log {\left (b x \right )} & \text {otherwise} \end {cases}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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