Optimal. Leaf size=19 \[ -\frac {\left (b x^2\right )^p}{(1-2 p) x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, 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}{(1-2 p) x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^p}{x^2} \, dx &=\left (x^{-2 p} \left (b x^2\right )^p\right ) \int x^{-2+2 p} \, dx\\ &=-\frac {\left (b x^2\right )^p}{(1-2 p) x}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} \frac {\left (b x^2\right )^p}{(-1+2 p) x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 19, normalized size = 1.00
method | result | size |
gosper | \(\frac {\left (b \,x^{2}\right )^{p}}{x \left (-1+2 p \right )}\) | \(19\) |
risch | \(\frac {\left (b \,x^{2}\right )^{p}}{x \left (-1+2 p \right )}\) | \(19\) |
norman | \(\frac {{\mathrm e}^{p \ln \left (b \,x^{2}\right )}}{\left (-1+2 p \right ) x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 19, normalized size = 1.00 \begin {gather*} \frac {b^{p} x^{2 \, p}}{{\left (2 \, p - 1\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 18, normalized size = 0.95 \begin {gather*} \frac {\left (b x^{2}\right )^{p}}{{\left (2 \, p - 1\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \begin {cases} \frac {\left (b x^{2}\right )^{p}}{2 p x - x} & \text {for}\: p \neq \frac {1}{2} \\\int \frac {\sqrt {b x^{2}}}{x^{2}}\, dx & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.93, size = 18, normalized size = 0.95 \begin {gather*} \frac {{\left (b\,x^2\right )}^p}{x\,\left (2\,p-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________