Optimal. Leaf size=30 \[ -\frac{4 \sqrt [4]{c+d x}}{\sqrt [4]{a+b x} (b c-a d)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0030378, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {37} \[ -\frac{4 \sqrt [4]{c+d x}}{\sqrt [4]{a+b x} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^{5/4} (c+d x)^{3/4}} \, dx &=-\frac{4 \sqrt [4]{c+d x}}{(b c-a d) \sqrt [4]{a+b x}}\\ \end{align*}
Mathematica [A] time = 0.0070169, size = 30, normalized size = 1. \[ \frac{4 \sqrt [4]{c+d x}}{\sqrt [4]{a+b x} (a d-b c)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 27, normalized size = 0.9 \begin{align*} 4\,{\frac{\sqrt [4]{dx+c}}{\sqrt [4]{bx+a} \left ( ad-bc \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x + a\right )}^{\frac{5}{4}}{\left (d x + c\right )}^{\frac{3}{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.31905, size = 97, normalized size = 3.23 \begin{align*} -\frac{4 \,{\left (b x + a\right )}^{\frac{3}{4}}{\left (d x + c\right )}^{\frac{1}{4}}}{a b c - a^{2} d +{\left (b^{2} c - a b d\right )} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (a + b x\right )^{\frac{5}{4}} \left (c + d x\right )^{\frac{3}{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]