Optimal. Leaf size=38 \[ \frac {(a+b x)^6 (A b-a B)}{6 b^2}+\frac {B (a+b x)^7}{7 b^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \[ \frac {(a+b x)^6 (A b-a B)}{6 b^2}+\frac {B (a+b x)^7}{7 b^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int (a+b x)^5 (A+B x) \, dx &=\int \left (\frac {(A b-a B) (a+b x)^5}{b}+\frac {B (a+b x)^6}{b}\right ) \, dx\\ &=\frac {(A b-a B) (a+b x)^6}{6 b^2}+\frac {B (a+b x)^7}{7 b^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.02, size = 109, normalized size = 2.87 \[ a^5 A x+\frac {1}{2} a^4 x^2 (a B+5 A b)+\frac {5}{3} a^3 b x^3 (a B+2 A b)+\frac {5}{2} a^2 b^2 x^4 (a B+A b)+\frac {1}{6} b^4 x^6 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac {1}{7} b^5 B x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.54, size = 121, normalized size = 3.18 \[ \frac {1}{7} x^{7} b^{5} B + \frac {5}{6} x^{6} b^{4} a B + \frac {1}{6} x^{6} b^{5} A + 2 x^{5} b^{3} a^{2} B + x^{5} b^{4} a A + \frac {5}{2} x^{4} b^{2} a^{3} B + \frac {5}{2} x^{4} b^{3} a^{2} A + \frac {5}{3} x^{3} b a^{4} B + \frac {10}{3} x^{3} b^{2} a^{3} A + \frac {1}{2} x^{2} a^{5} B + \frac {5}{2} x^{2} b a^{4} A + x a^{5} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.26, size = 121, normalized size = 3.18 \[ \frac {1}{7} \, B b^{5} x^{7} + \frac {5}{6} \, B a b^{4} x^{6} + \frac {1}{6} \, A b^{5} x^{6} + 2 \, B a^{2} b^{3} x^{5} + A a b^{4} x^{5} + \frac {5}{2} \, B a^{3} b^{2} x^{4} + \frac {5}{2} \, A a^{2} b^{3} x^{4} + \frac {5}{3} \, B a^{4} b x^{3} + \frac {10}{3} \, A a^{3} b^{2} x^{3} + \frac {1}{2} \, B a^{5} x^{2} + \frac {5}{2} \, A a^{4} b x^{2} + A a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 121, normalized size = 3.18 \[ \frac {B \,b^{5} x^{7}}{7}+A \,a^{5} x +\frac {\left (b^{5} A +5 a \,b^{4} B \right ) x^{6}}{6}+\frac {\left (5 a \,b^{4} A +10 a^{2} b^{3} B \right ) x^{5}}{5}+\frac {\left (10 a^{2} b^{3} A +10 a^{3} b^{2} B \right ) x^{4}}{4}+\frac {\left (10 a^{3} b^{2} A +5 a^{4} b B \right ) x^{3}}{3}+\frac {\left (5 a^{4} b A +a^{5} B \right ) x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.06, size = 115, normalized size = 3.03 \[ \frac {1}{7} \, B b^{5} x^{7} + A a^{5} x + \frac {1}{6} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{6} + {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{5} + \frac {5}{2} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{4} + \frac {5}{3} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{3} + \frac {1}{2} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 103, normalized size = 2.71 \[ x^2\,\left (\frac {B\,a^5}{2}+\frac {5\,A\,b\,a^4}{2}\right )+x^6\,\left (\frac {A\,b^5}{6}+\frac {5\,B\,a\,b^4}{6}\right )+\frac {B\,b^5\,x^7}{7}+A\,a^5\,x+\frac {5\,a^2\,b^2\,x^4\,\left (A\,b+B\,a\right )}{2}+\frac {5\,a^3\,b\,x^3\,\left (2\,A\,b+B\,a\right )}{3}+a\,b^3\,x^5\,\left (A\,b+2\,B\,a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.10, size = 129, normalized size = 3.39 \[ A a^{5} x + \frac {B b^{5} x^{7}}{7} + x^{6} \left (\frac {A b^{5}}{6} + \frac {5 B a b^{4}}{6}\right ) + x^{5} \left (A a b^{4} + 2 B a^{2} b^{3}\right ) + x^{4} \left (\frac {5 A a^{2} b^{3}}{2} + \frac {5 B a^{3} b^{2}}{2}\right ) + x^{3} \left (\frac {10 A a^{3} b^{2}}{3} + \frac {5 B a^{4} b}{3}\right ) + x^{2} \left (\frac {5 A a^{4} b}{2} + \frac {B a^{5}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________