Optimal. Leaf size=25 \[ a^2 x+\frac {2}{3} a b x^3+\frac {b^2 x^5}{5} \]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {1586} \begin {gather*} a^2 x+\frac {2}{3} a b x^3+\frac {b^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1586
Rubi steps
\begin {align*} \int \frac {a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{c+d x} \, dx &=\int \left (a^2+2 a b x^2+b^2 x^4\right ) \, dx\\ &=a^2 x+\frac {2}{3} a b x^3+\frac {b^2 x^5}{5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} a^2 x+\frac {2}{3} a b x^3+\frac {b^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.03, size = 26, normalized size = 1.04 \begin {gather*} \frac {1}{15} \left (15 a^2 x+10 a b x^3+3 b^2 x^5\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.79, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{5} \, b^{2} x^{5} + \frac {2}{3} \, a b x^{3} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.37, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{5} \, b^{2} x^{5} + \frac {2}{3} \, a b x^{3} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{5} b^{2} x^{5}+\frac {2}{3} a b \,x^{3}+a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.44, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{5} \, b^{2} x^{5} + \frac {2}{3} \, a b x^{3} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 21, normalized size = 0.84 \begin {gather*} a^2\,x+\frac {2\,a\,b\,x^3}{3}+\frac {b^2\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 22, normalized size = 0.88 \begin {gather*} a^{2} x + \frac {2 a b x^{3}}{3} + \frac {b^{2} x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________