Optimal. Leaf size=26 \[ -\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {270}
\begin {gather*} -\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int \frac {x^{-1-\frac {n}{2}}}{\sqrt {a+b x^n}} \, dx &=-\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 26, normalized size = 1.00 \begin {gather*} -\frac {2 x^{-n/2} \sqrt {a+b x^n}}{a n} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {x^{-1-\frac {n}{2}}}{\sqrt {a +b \,x^{n}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \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 [A]
time = 19.66, size = 22, normalized size = 0.85 \begin {gather*} - \frac {2 \sqrt {b} \sqrt {\frac {a x^{- n}}{b} + 1}}{a n} \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 = 1.31, size = 24, normalized size = 0.92 \begin {gather*} -\frac {2\,\sqrt {a+b\,x^n}}{a\,n\,x^{n/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________