Optimal. Leaf size=14 \[ \frac {(a+b x)^3}{3 b} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} \frac {(a+b x)^3}{3 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin {align*} \int (a+b x)^2 \, dx &=\frac {(a+b x)^3}{3 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {(a+b x)^3}{3 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b x)^2 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.22, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} x^{3} b^{2} + x^{2} b a + x a^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\left (b x + a\right )}^{3}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} \frac {\left (b x +a \right )^{3}}{3 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.08, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 20, normalized size = 1.43 \begin {gather*} a^2\,x+a\,b\,x^2+\frac {b^2\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.07, size = 19, normalized size = 1.36 \begin {gather*} a^{2} x + a b x^{2} + \frac {b^{2} x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________