Optimal. Leaf size=18 \[ \frac {x \left (a+b x^n\right )^{-1/n}}{a} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {191} \[ \frac {x \left (a+b x^n\right )^{-1/n}}{a} \]
Antiderivative was successfully verified.
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Rule 191
Rubi steps
\begin {align*} \int \left (a+b x^n\right )^{-\frac {1+n}{n}} \, dx &=\frac {x \left (a+b x^n\right )^{-1/n}}{a}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 18, normalized size = 1.00 \[ \frac {x \left (a+b x^n\right )^{-1/n}}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 31, normalized size = 1.72 \[ \frac {b x x^{n} + a x}{{\left (b x^{n} + a\right )}^{\frac {n + 1}{n}} a} \]
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 \[ \int \frac {1}{{\left (b x^{n} + a\right )}^{\frac {n + 1}{n}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 35, normalized size = 1.94 \[ \left (\frac {b x \,{\mathrm e}^{n \ln \relax (x )}}{a}+x \right ) {\mathrm e}^{\frac {\left (-n -1\right ) \ln \left (b \,{\mathrm e}^{n \ln \relax (x )}+a \right )}{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b x^{n} + a\right )}^{\frac {n + 1}{n}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.30, size = 75, normalized size = 4.17 \[ \frac {b\,x^{n+1}\,\left (\frac {a}{b\,x^n}-{\left (\frac {a}{b\,x^n}+1\right )}^{\frac {n+1}{n}}+1\right )}{a\,n\,\left (\frac {n+1}{n}-1\right )\,{\left (a+b\,x^n\right )}^{\frac {n+1}{n}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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