Optimal. Leaf size=38 \[ \frac {x^{m+1} \, _2F_1\left (1,\frac {m+1}{7};\frac {m+8}{7};\frac {b x^7}{a}\right )}{a (m+1)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {364} \[ \frac {x^{m+1} \, _2F_1\left (1,\frac {m+1}{7};\frac {m+8}{7};\frac {b x^7}{a}\right )}{a (m+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 364
Rubi steps
\begin {align*} \int \frac {x^m}{a-b x^7} \, dx &=\frac {x^{1+m} \, _2F_1\left (1,\frac {1+m}{7};\frac {8+m}{7};\frac {b x^7}{a}\right )}{a (1+m)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 40, normalized size = 1.05 \[ \frac {x^{m+1} \, _2F_1\left (1,\frac {m+1}{7};\frac {m+1}{7}+1;\frac {b x^7}{a}\right )}{a (m+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.65, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {x^{m}}{b x^{7} - a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {x^{m}}{b x^{7} - a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.14, size = 0, normalized size = 0.00 \[ \int \frac {x^{m}}{-b \,x^{7}+a}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ -\int \frac {x^{m}}{b x^{7} - a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {x^m}{a-b\,x^7} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________