Optimal. Leaf size=14 \[ \frac {\left (b x^n\right )^p}{n p} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {15, 30} \[ \frac {\left (b x^n\right )^p}{n p} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^n\right )^p}{x} \, dx &=\left (x^{-n p} \left (b x^n\right )^p\right ) \int x^{-1+n p} \, dx\\ &=\frac {\left (b x^n\right )^p}{n p}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {\left (b x^n\right )^p}{n p} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 18, normalized size = 1.29 \[ \frac {e^{\left (n p \log \relax (x) + p \log \relax (b)\right )}}{n p} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 1.00 \[ \frac {\left (b x^{n}\right )^{p}}{n p} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 1.07 \[ \frac {\left (b \,x^{n}\right )^{p}}{n p} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.42, size = 15, normalized size = 1.07 \[ \frac {b^{p} {\left (x^{n}\right )}^{p}}{n p} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\left (b\,x^n\right )}^p}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 22, normalized size = 1.57 \[ \begin {cases} \log {\relax (x )} & \text {for}\: p = 0 \wedge \left (n = 0 \vee p = 0\right ) \\b^{p} \log {\relax (x )} & \text {for}\: n = 0 \\\frac {b^{p} \left (x^{n}\right )^{p}}{n p} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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