Optimal. Leaf size=30 \[ -\frac {4 (7 x-1) \left (x^4-x^3\right )^{3/4}}{3 (x-1) x^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.16, antiderivative size = 36, normalized size of antiderivative = 1.20, number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {2056, 78, 37} \begin {gather*} \frac {4}{3 \sqrt [4]{x^4-x^3}}-\frac {28 x}{3 \sqrt [4]{x^4-x^3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 78
Rule 2056
Rubi steps
\begin {align*} \int \frac {1+x}{(-1+x) x \sqrt [4]{-x^3+x^4}} \, dx &=\frac {\left (\sqrt [4]{-1+x} x^{3/4}\right ) \int \frac {1+x}{(-1+x)^{5/4} x^{7/4}} \, dx}{\sqrt [4]{-x^3+x^4}}\\ &=\frac {4}{3 \sqrt [4]{-x^3+x^4}}+\frac {\left (7 \sqrt [4]{-1+x} x^{3/4}\right ) \int \frac {1}{(-1+x)^{5/4} x^{3/4}} \, dx}{3 \sqrt [4]{-x^3+x^4}}\\ &=\frac {4}{3 \sqrt [4]{-x^3+x^4}}-\frac {28 x}{3 \sqrt [4]{-x^3+x^4}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 0.67 \begin {gather*} -\frac {4 (7 x-1)}{3 \sqrt [4]{(x-1) x^3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.22, size = 30, normalized size = 1.00 \begin {gather*} -\frac {4 (-1+7 x) \left (-x^3+x^4\right )^{3/4}}{3 (-1+x) x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 18, normalized size = 0.60 \begin {gather*} -\frac {4 \, {\left (7 \, x - 1\right )}}{3 \, {\left (x^{4} - x^{3}\right )}^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.77, size = 23, normalized size = 0.77 \begin {gather*} \frac {4}{3} \, {\left (-\frac {1}{x} + 1\right )}^{\frac {3}{4}} + \frac {8}{{\left (-\frac {1}{x} + 1\right )}^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 17, normalized size = 0.57
method | result | size |
risch | \(-\frac {4 \left (-1+7 x \right )}{3 \left (x^{3} \left (-1+x \right )\right )^{\frac {1}{4}}}\) | \(17\) |
gosper | \(-\frac {4 \left (-1+7 x \right )}{3 \left (x^{4}-x^{3}\right )^{\frac {1}{4}}}\) | \(19\) |
trager | \(-\frac {4 \left (-1+7 x \right ) \left (x^{4}-x^{3}\right )^{\frac {3}{4}}}{3 \left (-1+x \right ) x^{3}}\) | \(27\) |
meijerg | \(\frac {4 \left (-\mathrm {signum}\left (-1+x \right )\right )^{\frac {1}{4}} \left (1-4 x \right )}{3 \mathrm {signum}\left (-1+x \right )^{\frac {1}{4}} \left (1-x \right )^{\frac {1}{4}} x^{\frac {3}{4}}}-\frac {4 \left (-\mathrm {signum}\left (-1+x \right )\right )^{\frac {1}{4}} x^{\frac {1}{4}}}{\mathrm {signum}\left (-1+x \right )^{\frac {1}{4}} \left (1-x \right )^{\frac {1}{4}}}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 1}{{\left (x^{4} - x^{3}\right )}^{\frac {1}{4}} {\left (x - 1\right )} x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.23, size = 18, normalized size = 0.60 \begin {gather*} -\frac {28\,x-4}{3\,{\left (x^4-x^3\right )}^{1/4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 1}{x \sqrt [4]{x^{3} \left (x - 1\right )} \left (x - 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________