Optimal. Leaf size=40 \[ -\frac {9}{4 \sqrt {2 x-1}}+\frac {7}{2 (2 x-1)^{3/2}}-\frac {49}{20 (2 x-1)^{5/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {43} \[ -\frac {9}{4 \sqrt {2 x-1}}+\frac {7}{2 (2 x-1)^{3/2}}-\frac {49}{20 (2 x-1)^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(-5+3 x)^2}{(-1+2 x)^{7/2}} \, dx &=\int \left (\frac {49}{4 (-1+2 x)^{7/2}}-\frac {21}{2 (-1+2 x)^{5/2}}+\frac {9}{4 (-1+2 x)^{3/2}}\right ) \, dx\\ &=-\frac {49}{20 (-1+2 x)^{5/2}}+\frac {7}{2 (-1+2 x)^{3/2}}-\frac {9}{4 \sqrt {-1+2 x}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 23, normalized size = 0.58 \[ \frac {-45 x^2+80 x-41}{5 (2 x-1)^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 36, normalized size = 0.90 \[ -\frac {{\left (45 \, x^{2} - 80 \, x + 41\right )} \sqrt {2 \, x - 1}}{5 \, {\left (8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.89, size = 23, normalized size = 0.58 \[ -\frac {45 \, {\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \, {\left (2 \, x - 1\right )}^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 20, normalized size = 0.50 \[ -\frac {45 x^{2}-80 x +41}{5 \left (2 x -1\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 23, normalized size = 0.58 \[ -\frac {45 \, {\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \, {\left (2 \, x - 1\right )}^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.35, size = 23, normalized size = 0.58 \[ -\frac {\frac {9\,{\left (2\,x-1\right )}^2}{4}-7\,x+\frac {119}{20}}{{\left (2\,x-1\right )}^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 1.39, size = 116, normalized size = 2.90 \[ - \frac {45 x^{2}}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} + \frac {80 x}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} - \frac {41}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________