Optimal. Leaf size=21 \[ -\frac {\left (b x^2\right )^p}{2 (1-p) x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 21, 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} \[ -\frac {\left (b x^2\right )^p}{2 (1-p) x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^p}{x^3} \, dx &=\left (x^{-2 p} \left (b x^2\right )^p\right ) \int x^{-3+2 p} \, dx\\ &=-\frac {\left (b x^2\right )^p}{2 (1-p) x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {\left (b x^2\right )^p}{(2 p-2) x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 17, normalized size = 0.81 \[ \frac {\left (b x^{2}\right )^{p}}{2 \, {\left (p - 1\right )} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x^{2}\right )^{p}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {\left (b \,x^{2}\right )^{p}}{2 \left (p -1\right ) x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 18, normalized size = 0.86 \[ \frac {b^{p} {\left (x^{2}\right )}^{p}}{2 \, {\left (p - 1\right )} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 18, normalized size = 0.86 \[ \frac {{\left (b\,x^2\right )}^p}{x^2\,\left (2\,p-2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 24, normalized size = 1.14 \[ \begin {cases} \frac {b^{p} \left (x^{2}\right )^{p}}{2 p x^{2} - 2 x^{2}} & \text {for}\: p \neq 1 \\b \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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