Optimal. Leaf size=45 \[ \frac {5 x^{4/5}}{4}-\frac {5 x^{3/5}}{3}+\frac {5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {190, 43} \[ \frac {5 x^{4/5}}{4}-\frac {5 x^{3/5}}{3}+\frac {5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 190
Rubi steps
\begin {align*} \int \frac {1}{1+\sqrt [5]{x}} \, dx &=5 \operatorname {Subst}\left (\int \frac {x^4}{1+x} \, dx,x,\sqrt [5]{x}\right )\\ &=5 \operatorname {Subst}\left (\int \left (-1+x-x^2+x^3+\frac {1}{1+x}\right ) \, dx,x,\sqrt [5]{x}\right )\\ &=-5 \sqrt [5]{x}+\frac {5 x^{2/5}}{2}-\frac {5 x^{3/5}}{3}+\frac {5 x^{4/5}}{4}+5 \log \left (1+\sqrt [5]{x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 45, normalized size = 1.00 \[ \frac {5 x^{4/5}}{4}-\frac {5 x^{3/5}}{3}+\frac {5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.61, size = 29, normalized size = 0.64 \[ \frac {5}{4} \, x^{\frac {4}{5}} - \frac {5}{3} \, x^{\frac {3}{5}} + \frac {5}{2} \, x^{\frac {2}{5}} - 5 \, x^{\frac {1}{5}} + 5 \, \log \left (x^{\frac {1}{5}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 29, normalized size = 0.64 \[ \frac {5}{4} \, x^{\frac {4}{5}} - \frac {5}{3} \, x^{\frac {3}{5}} + \frac {5}{2} \, x^{\frac {2}{5}} - 5 \, x^{\frac {1}{5}} + 5 \, \log \left (x^{\frac {1}{5}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.06, size = 79, normalized size = 1.76 \[ 4 \ln \left (x^{\frac {1}{5}}+1\right )+\ln \left (x +1\right )-\ln \left (2 x^{\frac {2}{5}}-\sqrt {5}\, x^{\frac {1}{5}}-x^{\frac {1}{5}}+2\right )-\ln \left (2 x^{\frac {2}{5}}+\sqrt {5}\, x^{\frac {1}{5}}-x^{\frac {1}{5}}+2\right )+\frac {5 x^{\frac {4}{5}}}{4}-\frac {5 x^{\frac {3}{5}}}{3}+\frac {5 x^{\frac {2}{5}}}{2}-5 x^{\frac {1}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 42, normalized size = 0.93 \[ \frac {5}{4} \, {\left (x^{\frac {1}{5}} + 1\right )}^{4} - \frac {20}{3} \, {\left (x^{\frac {1}{5}} + 1\right )}^{3} + 15 \, {\left (x^{\frac {1}{5}} + 1\right )}^{2} - 20 \, x^{\frac {1}{5}} + 5 \, \log \left (x^{\frac {1}{5}} + 1\right ) - 20 \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 29, normalized size = 0.64 \[ 5\,\ln \left (x^{1/5}+1\right )-5\,x^{1/5}+\frac {5\,x^{2/5}}{2}-\frac {5\,x^{3/5}}{3}+\frac {5\,x^{4/5}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 4.08, size = 41, normalized size = 0.91 \[ \frac {5 x^{\frac {4}{5}}}{4} - \frac {5 x^{\frac {3}{5}}}{3} + \frac {5 x^{\frac {2}{5}}}{2} - 5 \sqrt [5]{x} + 5 \log {\left (\sqrt [5]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________