Optimal. Leaf size=65 \[ 15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+15 a^4 b \sqrt [3]{x}+a^5 \log (x)+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0287267, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ 15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+15 a^4 b \sqrt [3]{x}+a^5 \log (x)+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^5}{x} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (5 a^4 b+\frac{a^5}{x}+10 a^3 b^2 x+10 a^2 b^3 x^2+5 a b^4 x^3+b^5 x^4\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=15 a^4 b \sqrt [3]{x}+15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3}+a^5 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0211744, size = 65, normalized size = 1. \[ 15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+15 a^4 b \sqrt [3]{x}+a^5 \log (x)+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 54, normalized size = 0.8 \begin{align*} 15\,{a}^{4}b\sqrt [3]{x}+15\,{a}^{3}{b}^{2}{x}^{2/3}+10\,{a}^{2}{b}^{3}x+{\frac{15\,a{b}^{4}}{4}{x}^{{\frac{4}{3}}}}+{\frac{3\,{b}^{5}}{5}{x}^{{\frac{5}{3}}}}+{a}^{5}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.976911, size = 72, normalized size = 1.11 \begin{align*} \frac{3}{5} \, b^{5} x^{\frac{5}{3}} + \frac{15}{4} \, a b^{4} x^{\frac{4}{3}} + 10 \, a^{2} b^{3} x + a^{5} \log \left (x\right ) + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 15 \, a^{4} b x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48146, size = 142, normalized size = 2.18 \begin{align*} 10 \, a^{2} b^{3} x + 3 \, a^{5} \log \left (x^{\frac{1}{3}}\right ) + \frac{3}{5} \,{\left (b^{5} x + 25 \, a^{3} b^{2}\right )} x^{\frac{2}{3}} + \frac{15}{4} \,{\left (a b^{4} x + 4 \, a^{4} b\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 19.843, size = 66, normalized size = 1.02 \begin{align*} a^{5} \log{\left (x \right )} + 15 a^{4} b \sqrt [3]{x} + 15 a^{3} b^{2} x^{\frac{2}{3}} + 10 a^{2} b^{3} x + \frac{15 a b^{4} x^{\frac{4}{3}}}{4} + \frac{3 b^{5} x^{\frac{5}{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19133, size = 73, normalized size = 1.12 \begin{align*} \frac{3}{5} \, b^{5} x^{\frac{5}{3}} + \frac{15}{4} \, a b^{4} x^{\frac{4}{3}} + 10 \, a^{2} b^{3} x + a^{5} \log \left ({\left | x \right |}\right ) + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 15 \, a^{4} b x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]