Optimal. Leaf size=65 \[ \frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} (A b+a C) x^4+\frac {1}{5} (b B+a D) x^5+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1816}
\begin {gather*} \frac {1}{4} x^4 (a C+A b)+\frac {1}{2} a A x^2+\frac {1}{5} x^5 (a D+b B)+\frac {1}{3} a B x^3+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1816
Rubi steps
\begin {align*} \int x \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx &=\int \left (a A x+a B x^2+(A b+a C) x^3+(b B+a D) x^4+b C x^5+b D x^6\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} (A b+a C) x^4+\frac {1}{5} (b B+a D) x^5+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 65, normalized size = 1.00 \begin {gather*} \frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} (A b+a C) x^4+\frac {1}{5} (b B+a D) x^5+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 54, normalized size = 0.83
method | result | size |
default | \(\frac {a A \,x^{2}}{2}+\frac {B a \,x^{3}}{3}+\frac {\left (A b +a C \right ) x^{4}}{4}+\frac {\left (B b +a D\right ) x^{5}}{5}+\frac {b C \,x^{6}}{6}+\frac {b D x^{7}}{7}\) | \(54\) |
norman | \(\frac {b D x^{7}}{7}+\frac {b C \,x^{6}}{6}+\left (\frac {B b}{5}+\frac {a D}{5}\right ) x^{5}+\left (\frac {A b}{4}+\frac {a C}{4}\right ) x^{4}+\frac {B a \,x^{3}}{3}+\frac {a A \,x^{2}}{2}\) | \(56\) |
gosper | \(\frac {1}{7} b D x^{7}+\frac {1}{6} b C \,x^{6}+\frac {1}{5} b B \,x^{5}+\frac {1}{5} x^{5} a D+\frac {1}{4} x^{4} A b +\frac {1}{4} x^{4} a C +\frac {1}{3} B a \,x^{3}+\frac {1}{2} a A \,x^{2}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 53, normalized size = 0.82 \begin {gather*} \frac {1}{7} \, D b x^{7} + \frac {1}{6} \, C b x^{6} + \frac {1}{5} \, {\left (D a + B b\right )} x^{5} + \frac {1}{3} \, B a x^{3} + \frac {1}{4} \, {\left (C a + A b\right )} x^{4} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 5.12, size = 53, normalized size = 0.82 \begin {gather*} \frac {1}{7} \, D b x^{7} + \frac {1}{6} \, C b x^{6} + \frac {1}{5} \, {\left (D a + B b\right )} x^{5} + \frac {1}{3} \, B a x^{3} + \frac {1}{4} \, {\left (C a + A b\right )} x^{4} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 60, normalized size = 0.92 \begin {gather*} \frac {A a x^{2}}{2} + \frac {B a x^{3}}{3} + \frac {C b x^{6}}{6} + \frac {D b x^{7}}{7} + x^{5} \left (\frac {B b}{5} + \frac {D a}{5}\right ) + x^{4} \left (\frac {A b}{4} + \frac {C a}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.55, size = 57, normalized size = 0.88 \begin {gather*} \frac {1}{7} \, D b x^{7} + \frac {1}{6} \, C b x^{6} + \frac {1}{5} \, D a x^{5} + \frac {1}{5} \, B b x^{5} + \frac {1}{4} \, C a x^{4} + \frac {1}{4} \, A b x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.19, size = 57, normalized size = 0.88 \begin {gather*} \frac {a\,x^5\,D}{5}+\frac {b\,x^7\,D}{7}+\frac {A\,a\,x^2}{2}+\frac {B\,a\,x^3}{3}+\frac {A\,b\,x^4}{4}+\frac {C\,a\,x^4}{4}+\frac {B\,b\,x^5}{5}+\frac {C\,b\,x^6}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________