Optimal. Leaf size=92 \[ \frac{128 b^3 \left (a+b x^4\right )^{9/4}}{13923 a^4 x^9}-\frac{32 b^2 \left (a+b x^4\right )^{9/4}}{1547 a^3 x^{13}}+\frac{4 b \left (a+b x^4\right )^{9/4}}{119 a^2 x^{17}}-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.028267, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {271, 264} \[ \frac{128 b^3 \left (a+b x^4\right )^{9/4}}{13923 a^4 x^9}-\frac{32 b^2 \left (a+b x^4\right )^{9/4}}{1547 a^3 x^{13}}+\frac{4 b \left (a+b x^4\right )^{9/4}}{119 a^2 x^{17}}-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 271
Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^4\right )^{5/4}}{x^{22}} \, dx &=-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}}-\frac{(4 b) \int \frac{\left (a+b x^4\right )^{5/4}}{x^{18}} \, dx}{7 a}\\ &=-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}}+\frac{4 b \left (a+b x^4\right )^{9/4}}{119 a^2 x^{17}}+\frac{\left (32 b^2\right ) \int \frac{\left (a+b x^4\right )^{5/4}}{x^{14}} \, dx}{119 a^2}\\ &=-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}}+\frac{4 b \left (a+b x^4\right )^{9/4}}{119 a^2 x^{17}}-\frac{32 b^2 \left (a+b x^4\right )^{9/4}}{1547 a^3 x^{13}}-\frac{\left (128 b^3\right ) \int \frac{\left (a+b x^4\right )^{5/4}}{x^{10}} \, dx}{1547 a^3}\\ &=-\frac{\left (a+b x^4\right )^{9/4}}{21 a x^{21}}+\frac{4 b \left (a+b x^4\right )^{9/4}}{119 a^2 x^{17}}-\frac{32 b^2 \left (a+b x^4\right )^{9/4}}{1547 a^3 x^{13}}+\frac{128 b^3 \left (a+b x^4\right )^{9/4}}{13923 a^4 x^9}\\ \end{align*}
Mathematica [A] time = 0.0146056, size = 53, normalized size = 0.58 \[ \frac{\left (a+b x^4\right )^{9/4} \left (468 a^2 b x^4-663 a^3-288 a b^2 x^8+128 b^3 x^{12}\right )}{13923 a^4 x^{21}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 50, normalized size = 0.5 \begin{align*} -{\frac{-128\,{b}^{3}{x}^{12}+288\,a{b}^{2}{x}^{8}-468\,{a}^{2}b{x}^{4}+663\,{a}^{3}}{13923\,{x}^{21}{a}^{4}} \left ( b{x}^{4}+a \right ) ^{{\frac{9}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.966351, size = 93, normalized size = 1.01 \begin{align*} \frac{\frac{1547 \,{\left (b x^{4} + a\right )}^{\frac{9}{4}} b^{3}}{x^{9}} - \frac{3213 \,{\left (b x^{4} + a\right )}^{\frac{13}{4}} b^{2}}{x^{13}} + \frac{2457 \,{\left (b x^{4} + a\right )}^{\frac{17}{4}} b}{x^{17}} - \frac{663 \,{\left (b x^{4} + a\right )}^{\frac{21}{4}}}{x^{21}}}{13923 \, a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.58285, size = 176, normalized size = 1.91 \begin{align*} \frac{{\left (128 \, b^{5} x^{20} - 32 \, a b^{4} x^{16} + 20 \, a^{2} b^{3} x^{12} - 15 \, a^{3} b^{2} x^{8} - 858 \, a^{4} b x^{4} - 663 \, a^{5}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{13923 \, a^{4} x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 36.2823, size = 954, normalized size = 10.37 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.12364, size = 541, normalized size = 5.88 \begin{align*} \frac{\frac{21 \,{\left (\frac{663 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}}{\left (b + \frac{a}{x^{4}}\right )} b^{3}}{x} - \frac{1105 \,{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{2}}{x^{9}} + \frac{765 \,{\left (b^{3} x^{12} + 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{4} + a^{3}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}} b}{x^{13}} - \frac{195 \,{\left (b^{4} x^{16} + 4 \, a b^{3} x^{12} + 6 \, a^{2} b^{2} x^{8} + 4 \, a^{3} b x^{4} + a^{4}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{x^{17}}\right )} b}{a^{3}} - \frac{\frac{13923 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}}{\left (b + \frac{a}{x^{4}}\right )} b^{4}}{x} - \frac{30940 \,{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{3}}{x^{9}} + \frac{32130 \,{\left (b^{3} x^{12} + 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{4} + a^{3}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{2}}{x^{13}} - \frac{16380 \,{\left (b^{4} x^{16} + 4 \, a b^{3} x^{12} + 6 \, a^{2} b^{2} x^{8} + 4 \, a^{3} b x^{4} + a^{4}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}} b}{x^{17}} + \frac{3315 \,{\left (b^{5} x^{20} + 5 \, a b^{4} x^{16} + 10 \, a^{2} b^{3} x^{12} + 10 \, a^{3} b^{2} x^{8} + 5 \, a^{4} b x^{4} + a^{5}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{x^{21}}}{a^{3}}}{69615 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]