Optimal. Leaf size=44 \[ \frac {4 b \left (a+b x^4\right )^{9/4}}{117 a^2 x^9}-\frac {\left (a+b x^4\right )^{9/4}}{13 a x^{13}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {271, 264} \[ \frac {4 b \left (a+b x^4\right )^{9/4}}{117 a^2 x^9}-\frac {\left (a+b x^4\right )^{9/4}}{13 a x^{13}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rule 271
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^{5/4}}{x^{14}} \, dx &=-\frac {\left (a+b x^4\right )^{9/4}}{13 a x^{13}}-\frac {(4 b) \int \frac {\left (a+b x^4\right )^{5/4}}{x^{10}} \, dx}{13 a}\\ &=-\frac {\left (a+b x^4\right )^{9/4}}{13 a x^{13}}+\frac {4 b \left (a+b x^4\right )^{9/4}}{117 a^2 x^9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 0.70 \[ \frac {\left (a+b x^4\right )^{9/4} \left (4 b x^4-9 a\right )}{117 a^2 x^{13}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.88, size = 49, normalized size = 1.11 \[ \frac {{\left (4 \, b^{3} x^{12} - a b^{2} x^{8} - 14 \, a^{2} b x^{4} - 9 \, a^{3}\right )} {\left (b x^{4} + a\right )}^{\frac {1}{4}}}{117 \, a^{2} x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x^{4} + a\right )}^{\frac {5}{4}}}{x^{14}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 28, normalized size = 0.64 \[ -\frac {\left (b \,x^{4}+a \right )^{\frac {9}{4}} \left (-4 b \,x^{4}+9 a \right )}{117 a^{2} x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.31, size = 35, normalized size = 0.80 \[ \frac {\frac {13 \, {\left (b x^{4} + a\right )}^{\frac {9}{4}} b}{x^{9}} - \frac {9 \, {\left (b x^{4} + a\right )}^{\frac {13}{4}}}{x^{13}}}{117 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.74, size = 71, normalized size = 1.61 \[ \frac {4\,b^3\,{\left (b\,x^4+a\right )}^{1/4}}{117\,a^2\,x}-\frac {14\,b\,{\left (b\,x^4+a\right )}^{1/4}}{117\,x^9}-\frac {a\,{\left (b\,x^4+a\right )}^{1/4}}{13\,x^{13}}-\frac {b^2\,{\left (b\,x^4+a\right )}^{1/4}}{117\,a\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 5.33, size = 148, normalized size = 3.36 \[ - \frac {9 a \sqrt [4]{b} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {13}{4}\right )}{16 x^{12} \Gamma \left (- \frac {5}{4}\right )} - \frac {7 b^{\frac {5}{4}} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {13}{4}\right )}{8 x^{8} \Gamma \left (- \frac {5}{4}\right )} - \frac {b^{\frac {9}{4}} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {13}{4}\right )}{16 a x^{4} \Gamma \left (- \frac {5}{4}\right )} + \frac {b^{\frac {13}{4}} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {13}{4}\right )}{4 a^{2} \Gamma \left (- \frac {5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________