Optimal. Leaf size=47 \[ -\frac{a^2}{9 b^3 (a+b x)^9}+\frac{a}{4 b^3 (a+b x)^8}-\frac{1}{7 b^3 (a+b x)^7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0207929, antiderivative size = 47, normalized size of antiderivative = 1., 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} \[ -\frac{a^2}{9 b^3 (a+b x)^9}+\frac{a}{4 b^3 (a+b x)^8}-\frac{1}{7 b^3 (a+b x)^7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{x^2}{(a+b x)^{10}} \, dx &=\int \left (\frac{a^2}{b^2 (a+b x)^{10}}-\frac{2 a}{b^2 (a+b x)^9}+\frac{1}{b^2 (a+b x)^8}\right ) \, dx\\ &=-\frac{a^2}{9 b^3 (a+b x)^9}+\frac{a}{4 b^3 (a+b x)^8}-\frac{1}{7 b^3 (a+b x)^7}\\ \end{align*}
Mathematica [A] time = 0.0146774, size = 31, normalized size = 0.66 \[ -\frac{a^2+9 a b x+36 b^2 x^2}{252 b^3 (a+b x)^9} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 42, normalized size = 0.9 \begin{align*} -{\frac{{a}^{2}}{9\,{b}^{3} \left ( bx+a \right ) ^{9}}}+{\frac{a}{4\,{b}^{3} \left ( bx+a \right ) ^{8}}}-{\frac{1}{7\,{b}^{3} \left ( bx+a \right ) ^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.04763, size = 162, normalized size = 3.45 \begin{align*} -\frac{36 \, b^{2} x^{2} + 9 \, a b x + a^{2}}{252 \,{\left (b^{12} x^{9} + 9 \, a b^{11} x^{8} + 36 \, a^{2} b^{10} x^{7} + 84 \, a^{3} b^{9} x^{6} + 126 \, a^{4} b^{8} x^{5} + 126 \, a^{5} b^{7} x^{4} + 84 \, a^{6} b^{6} x^{3} + 36 \, a^{7} b^{5} x^{2} + 9 \, a^{8} b^{4} x + a^{9} b^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.47967, size = 259, normalized size = 5.51 \begin{align*} -\frac{36 \, b^{2} x^{2} + 9 \, a b x + a^{2}}{252 \,{\left (b^{12} x^{9} + 9 \, a b^{11} x^{8} + 36 \, a^{2} b^{10} x^{7} + 84 \, a^{3} b^{9} x^{6} + 126 \, a^{4} b^{8} x^{5} + 126 \, a^{5} b^{7} x^{4} + 84 \, a^{6} b^{6} x^{3} + 36 \, a^{7} b^{5} x^{2} + 9 \, a^{8} b^{4} x + a^{9} b^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 1.10751, size = 128, normalized size = 2.72 \begin{align*} - \frac{a^{2} + 9 a b x + 36 b^{2} x^{2}}{252 a^{9} b^{3} + 2268 a^{8} b^{4} x + 9072 a^{7} b^{5} x^{2} + 21168 a^{6} b^{6} x^{3} + 31752 a^{5} b^{7} x^{4} + 31752 a^{4} b^{8} x^{5} + 21168 a^{3} b^{9} x^{6} + 9072 a^{2} b^{10} x^{7} + 2268 a b^{11} x^{8} + 252 b^{12} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20627, size = 39, normalized size = 0.83 \begin{align*} -\frac{36 \, b^{2} x^{2} + 9 \, a b x + a^{2}}{252 \,{\left (b x + a\right )}^{9} b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]