Optimal. Leaf size=35 \[ a^3 x+a^2 b x^3+\frac {3}{5} a b^2 x^5+\frac {b^3 x^7}{7} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {194} \begin {gather*} a^2 b x^3+a^3 x+\frac {3}{5} a b^2 x^5+\frac {b^3 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 194
Rubi steps
\begin {align*} \int \left (a+b x^2\right )^3 \, dx &=\int \left (a^3+3 a^2 b x^2+3 a b^2 x^4+b^3 x^6\right ) \, dx\\ &=a^3 x+a^2 b x^3+\frac {3}{5} a b^2 x^5+\frac {b^3 x^7}{7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 35, normalized size = 1.00 \begin {gather*} a^3 x+a^2 b x^3+\frac {3}{5} a b^2 x^5+\frac {b^3 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+b x^2\right )^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.02, size = 31, normalized size = 0.89 \begin {gather*} \frac {1}{7} x^{7} b^{3} + \frac {3}{5} x^{5} b^{2} a + x^{3} b a^{2} + x a^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.72, size = 31, normalized size = 0.89 \begin {gather*} \frac {1}{7} \, b^{3} x^{7} + \frac {3}{5} \, a b^{2} x^{5} + a^{2} b x^{3} + a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 32, normalized size = 0.91 \begin {gather*} \frac {1}{7} b^{3} x^{7}+\frac {3}{5} a \,b^{2} x^{5}+a^{2} b \,x^{3}+a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.36, size = 31, normalized size = 0.89 \begin {gather*} \frac {1}{7} \, b^{3} x^{7} + \frac {3}{5} \, a b^{2} x^{5} + a^{2} b x^{3} + a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 31, normalized size = 0.89 \begin {gather*} a^3\,x+a^2\,b\,x^3+\frac {3\,a\,b^2\,x^5}{5}+\frac {b^3\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 32, normalized size = 0.91 \begin {gather*} a^{3} x + a^{2} b x^{3} + \frac {3 a b^{2} x^{5}}{5} + \frac {b^{3} x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________