Optimal. Leaf size=55 \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0238052, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08, Rules used = {27, 76} \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 76
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a^2+2 a b x+b^2 x^2\right )}{x^7} \, dx &=\int \frac{(a+b x)^2 (A+B x)}{x^7} \, dx\\ &=\int \left (\frac{a^2 A}{x^7}+\frac{a (2 A b+a B)}{x^6}+\frac{b (A b+2 a B)}{x^5}+\frac{b^2 B}{x^4}\right ) \, dx\\ &=-\frac{a^2 A}{6 x^6}-\frac{a (2 A b+a B)}{5 x^5}-\frac{b (A b+2 a B)}{4 x^4}-\frac{b^2 B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0156567, size = 50, normalized size = 0.91 \[ -\frac{2 a^2 (5 A+6 B x)+6 a b x (4 A+5 B x)+5 b^2 x^2 (3 A+4 B x)}{60 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 48, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{2}}{6\,{x}^{6}}}-{\frac{a \left ( 2\,Ab+aB \right ) }{5\,{x}^{5}}}-{\frac{b \left ( Ab+2\,aB \right ) }{4\,{x}^{4}}}-{\frac{{b}^{2}B}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.982828, size = 69, normalized size = 1.25 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.31105, size = 120, normalized size = 2.18 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.27759, size = 54, normalized size = 0.98 \begin{align*} - \frac{10 A a^{2} + 20 B b^{2} x^{3} + x^{2} \left (15 A b^{2} + 30 B a b\right ) + x \left (24 A a b + 12 B a^{2}\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.12546, size = 69, normalized size = 1.25 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]