Optimal. Leaf size=16 \[ -\frac {\log \left (a-b x^7\right )}{7 b} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 16, 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 = {266}
\begin {gather*} -\frac {\log \left (a-b x^7\right )}{7 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rubi steps
\begin {align*} \int \frac {x^6}{a-b x^7} \, dx &=-\frac {\log \left (a-b x^7\right )}{7 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\log \left (a-b x^7\right )}{7 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.16, size = 15, normalized size = 0.94
method | result | size |
derivativedivides | \(-\frac {\ln \left (-b \,x^{7}+a \right )}{7 b}\) | \(15\) |
default | \(-\frac {\ln \left (-b \,x^{7}+a \right )}{7 b}\) | \(15\) |
norman | \(-\frac {\ln \left (-b \,x^{7}+a \right )}{7 b}\) | \(15\) |
risch | \(-\frac {\ln \left (-b \,x^{7}+a \right )}{7 b}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 15, normalized size = 0.94 \begin {gather*} -\frac {\log \left (b x^{7} - a\right )}{7 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 15, normalized size = 0.94 \begin {gather*} -\frac {\log \left (b x^{7} - a\right )}{7 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 12, normalized size = 0.75 \begin {gather*} - \frac {\log {\left (- a + b x^{7} \right )}}{7 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.53, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\log \left ({\left | b x^{7} - a \right |}\right )}{7 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 15, normalized size = 0.94 \begin {gather*} -\frac {\ln \left (b\,x^7-a\right )}{7\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________