Optimal. Leaf size=28 \[ a A x+\frac {1}{3} (A b+a B) x^3+\frac {1}{5} b B x^5 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {380}
\begin {gather*} \frac {1}{3} x^3 (a B+A b)+a A x+\frac {1}{5} b B x^5 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 380
Rubi steps
\begin {align*} \int \left (a+b x^2\right ) \left (A+B x^2\right ) \, dx &=\int \left (a A+(A b+a B) x^2+b B x^4\right ) \, dx\\ &=a A x+\frac {1}{3} (A b+a B) x^3+\frac {1}{5} b B x^5\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} a A x+\frac {1}{3} (A b+a B) x^3+\frac {1}{5} b B x^5 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 25, normalized size = 0.89
method | result | size |
default | \(a A x +\frac {\left (A b +B a \right ) x^{3}}{3}+\frac {b B \,x^{5}}{5}\) | \(25\) |
norman | \(\frac {b B \,x^{5}}{5}+\left (\frac {A b}{3}+\frac {B a}{3}\right ) x^{3}+a A x\) | \(26\) |
gosper | \(\frac {1}{5} b B \,x^{5}+\frac {1}{3} x^{3} A b +\frac {1}{3} x^{3} B a +a A x\) | \(27\) |
risch | \(\frac {1}{5} b B \,x^{5}+\frac {1}{3} x^{3} A b +\frac {1}{3} x^{3} B a +a A x\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, {\left (B a + A b\right )} x^{3} + A a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.83, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, {\left (B a + A b\right )} x^{3} + A a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 26, normalized size = 0.93 \begin {gather*} A a x + \frac {B b x^{5}}{5} + x^{3} \left (\frac {A b}{3} + \frac {B a}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.46, size = 26, normalized size = 0.93 \begin {gather*} \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, B a x^{3} + \frac {1}{3} \, A b x^{3} + A a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 25, normalized size = 0.89 \begin {gather*} \frac {B\,b\,x^5}{5}+\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^3+A\,a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________