Optimal. Leaf size=24 \[ -\frac {2 b x^{-2+n} \sqrt {b x^n}}{4-3 n} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30}
\begin {gather*} -\frac {2 b x^{n-2} \sqrt {b x^n}}{4-3 n} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^n\right )^{3/2}}{x^3} \, dx &=\left (b x^{-n/2} \sqrt {b x^n}\right ) \int x^{-3+\frac {3 n}{2}} \, dx\\ &=-\frac {2 b x^{-2+n} \sqrt {b x^n}}{4-3 n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 22, normalized size = 0.92 \begin {gather*} \frac {\left (b x^n\right )^{3/2}}{\left (-2+\frac {3 n}{2}\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 20, normalized size = 0.83
method | result | size |
gosper | \(\frac {2 \left (b \,x^{n}\right )^{\frac {3}{2}}}{x^{2} \left (-4+3 n \right )}\) | \(20\) |
risch | \(\frac {2 b^{2} x^{2 n}}{\left (-4+3 n \right ) x^{2} \sqrt {b \,x^{n}}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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 {2 \left (b x^{n}\right )^{\frac {3}{2}}}{3 n x^{2} - 4 x^{2}} & \text {for}\: n \neq \frac {4}{3} \\\int \frac {\left (b x^{\frac {4}{3}}\right )^{\frac {3}{2}}}{x^{3}}\, 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 = 0.96, size = 22, normalized size = 0.92 \begin {gather*} \frac {2\,b\,x^{n-2}\,\sqrt {b\,x^n}}{3\,n-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________