Optimal. Leaf size=19 \[ -\frac {\left (b x^2\right )^p}{(3-2 p) x^3} \]
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Rubi [A] time = 0.01, antiderivative size = 19, 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} \begin {gather*} -\frac {\left (b x^2\right )^p}{(3-2 p) x^3} \end {gather*}
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^4} \, dx &=\left (x^{-2 p} \left (b x^2\right )^p\right ) \int x^{-4+2 p} \, dx\\ &=-\frac {\left (b x^2\right )^p}{(3-2 p) x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} \frac {\left (b x^2\right )^p}{(2 p-3) x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.04, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (b x^2\right )^p}{x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.01, size = 18, normalized size = 0.95 \begin {gather*} \frac {\left (b x^{2}\right )^{p}}{{\left (2 \, p - 3\right )} x^{3}} \end {gather*}
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 \begin {gather*} \int \frac {\left (b x^{2}\right )^{p}}{x^{4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {\left (b \,x^{2}\right )^{p}}{\left (2 p -3\right ) x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 19, normalized size = 1.00 \begin {gather*} \frac {b^{p} x^{2 \, p}}{{\left (2 \, p - 3\right )} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.97, size = 18, normalized size = 0.95 \begin {gather*} \frac {{\left (b\,x^2\right )}^p}{x^3\,\left (2\,p-3\right )} \end {gather*}
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 {gather*} \begin {cases} \frac {b^{p} \left (x^{2}\right )^{p}}{2 p x^{3} - 3 x^{3}} & \text {for}\: p \neq \frac {3}{2} \\\int \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{x^{4}}\, dx & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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