Optimal. Leaf size=65 \[ \frac {f^{a+b x^3} \left (b^4 x^{12} \log ^4(f)-4 b^3 x^9 \log ^3(f)+12 b^2 x^6 \log ^2(f)-24 b x^3 \log (f)+24\right )}{3 b^5 \log ^5(f)} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.37, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2218} \[ \frac {f^a \text {Gamma}\left (5,-b x^3 \log (f)\right )}{3 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin {align*} \int f^{a+b x^3} x^{14} \, dx &=\frac {f^a \Gamma \left (5,-b x^3 \log (f)\right )}{3 b^5 \log ^5(f)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 0.00, size = 24, normalized size = 0.37 \[ \frac {f^a \Gamma \left (5,-b x^3 \log (f)\right )}{3 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 63, normalized size = 0.97 \[ \frac {{\left (b^{4} x^{12} \log \relax (f)^{4} - 4 \, b^{3} x^{9} \log \relax (f)^{3} + 12 \, b^{2} x^{6} \log \relax (f)^{2} - 24 \, b x^{3} \log \relax (f) + 24\right )} f^{b x^{3} + a}}{3 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.28, size = 105, normalized size = 1.62 \[ \frac {b^{4} f^{b x^{3}} f^{a} x^{12} \log \relax (f)^{4} - 4 \, b^{3} f^{b x^{3}} f^{a} x^{9} \log \relax (f)^{3} + 12 \, b^{2} f^{b x^{3}} f^{a} x^{6} \log \relax (f)^{2} - 24 \, b f^{b x^{3}} f^{a} x^{3} \log \relax (f) + 24 \, f^{b x^{3}} f^{a}}{3 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 64, normalized size = 0.98 \[ \frac {\left (b^{4} x^{12} \ln \relax (f )^{4}-4 b^{3} x^{9} \ln \relax (f )^{3}+12 b^{2} x^{6} \ln \relax (f )^{2}-24 b \,x^{3} \ln \relax (f )+24\right ) f^{b \,x^{3}+a}}{3 b^{5} \ln \relax (f )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.93, size = 77, normalized size = 1.18 \[ \frac {{\left (b^{4} f^{a} x^{12} \log \relax (f)^{4} - 4 \, b^{3} f^{a} x^{9} \log \relax (f)^{3} + 12 \, b^{2} f^{a} x^{6} \log \relax (f)^{2} - 24 \, b f^{a} x^{3} \log \relax (f) + 24 \, f^{a}\right )} f^{b x^{3}}}{3 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.54, size = 63, normalized size = 0.97 \[ \frac {f^{b\,x^3+a}\,\left (\frac {b^4\,x^{12}\,{\ln \relax (f)}^4}{3}-\frac {4\,b^3\,x^9\,{\ln \relax (f)}^3}{3}+4\,b^2\,x^6\,{\ln \relax (f)}^2-8\,b\,x^3\,\ln \relax (f)+8\right )}{b^5\,{\ln \relax (f)}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 82, normalized size = 1.26 \[ \begin {cases} \frac {f^{a + b x^{3}} \left (b^{4} x^{12} \log {\relax (f )}^{4} - 4 b^{3} x^{9} \log {\relax (f )}^{3} + 12 b^{2} x^{6} \log {\relax (f )}^{2} - 24 b x^{3} \log {\relax (f )} + 24\right )}{3 b^{5} \log {\relax (f )}^{5}} & \text {for}\: 3 b^{5} \log {\relax (f )}^{5} \neq 0 \\\frac {x^{15}}{15} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________