Optimal. Leaf size=36 \[ \frac {6}{1-x}-\frac {6}{(1-x)^2}+\frac {8}{3 (1-x)^3}+\log (1-x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ \frac {6}{1-x}-\frac {6}{(1-x)^2}+\frac {8}{3 (1-x)^3}+\log (1-x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(1+x)^3}{(-1+x)^4} \, dx &=\int \left (\frac {8}{(-1+x)^4}+\frac {12}{(-1+x)^3}+\frac {6}{(-1+x)^2}+\frac {1}{-1+x}\right ) \, dx\\ &=\frac {8}{3 (1-x)^3}-\frac {6}{(1-x)^2}+\frac {6}{1-x}+\log (1-x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 24, normalized size = 0.67 \[ \log (x-1)-\frac {2 \left (9 x^2-9 x+4\right )}{3 (x-1)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 46, normalized size = 1.28 \[ -\frac {18 \, x^{2} - 3 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )} \log \left (x - 1\right ) - 18 \, x + 8}{3 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.01, size = 23, normalized size = 0.64 \[ -\frac {2 \, {\left (9 \, x^{2} - 9 \, x + 4\right )}}{3 \, {\left (x - 1\right )}^{3}} + \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 27, normalized size = 0.75 \[ \ln \left (x -1\right )-\frac {6}{\left (x -1\right )^{2}}-\frac {6}{x -1}-\frac {8}{3 \left (x -1\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 32, normalized size = 0.89 \[ -\frac {2 \, {\left (9 \, x^{2} - 9 \, x + 4\right )}}{3 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.12, size = 22, normalized size = 0.61 \[ \ln \left (x-1\right )-\frac {6\,x^2-6\,x+\frac {8}{3}}{{\left (x-1\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 29, normalized size = 0.81 \[ \frac {- 18 x^{2} + 18 x - 8}{3 x^{3} - 9 x^{2} + 9 x - 3} + \log {\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________