Optimal. Leaf size=18 \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0041643, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int x^3 \left (a+b x^4\right )^{5/4} \, dx &=\frac{\left (a+b x^4\right )^{9/4}}{9 b}\\ \end{align*}
Mathematica [A] time = 0.0044347, size = 18, normalized size = 1. \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 15, normalized size = 0.8 \begin{align*}{\frac{1}{9\,b} \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 = 0.958315, size = 19, normalized size = 1.06 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.64556, size = 72, normalized size = 4. \begin{align*} \frac{{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 4.66337, size = 61, normalized size = 3.39 \begin{align*} \begin{cases} \frac{a^{2} \sqrt [4]{a + b x^{4}}}{9 b} + \frac{2 a x^{4} \sqrt [4]{a + b x^{4}}}{9} + \frac{b x^{8} \sqrt [4]{a + b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{4}}{4} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10771, size = 19, normalized size = 1.06 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]