Optimal. Leaf size=42 \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0178049, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+84 x-227 x^2-682 x^3+109 x^4+1380 x^5+900 x^6\right ) \, dx\\ &=36 x+42 x^2-\frac{227 x^3}{3}-\frac{341 x^4}{2}+\frac{109 x^5}{5}+230 x^6+\frac{900 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0011879, size = 42, normalized size = 1. \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 36\,x+42\,{x}^{2}-{\frac{227\,{x}^{3}}{3}}-{\frac{341\,{x}^{4}}{2}}+{\frac{109\,{x}^{5}}{5}}+230\,{x}^{6}+{\frac{900\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.22729, size = 46, normalized size = 1.1 \begin{align*} \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.31159, size = 99, normalized size = 2.36 \begin{align*} \frac{900}{7} x^{7} + 230 x^{6} + \frac{109}{5} x^{5} - \frac{341}{2} x^{4} - \frac{227}{3} x^{3} + 42 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.062157, size = 39, normalized size = 0.93 \begin{align*} \frac{900 x^{7}}{7} + 230 x^{6} + \frac{109 x^{5}}{5} - \frac{341 x^{4}}{2} - \frac{227 x^{3}}{3} + 42 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.775, size = 46, normalized size = 1.1 \begin{align*} \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]