Optimal. Leaf size=30 \[ \frac {b^2 x^3}{3}+\frac {1}{2} b c x^4+\frac {c^2 x^5}{5} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {611} \begin {gather*} \frac {b^2 x^3}{3}+\frac {1}{2} b c x^4+\frac {c^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 611
Rubi steps
\begin {align*} \int \left (b x+c x^2\right )^2 \, dx &=\int \left (b^2 x^2+2 b c x^3+c^2 x^4\right ) \, dx\\ &=\frac {b^2 x^3}{3}+\frac {1}{2} b c x^4+\frac {c^2 x^5}{5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {b^2 x^3}{3}+\frac {1}{2} b c x^4+\frac {c^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (b x+c x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.36, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{5} x^{5} c^{2} + \frac {1}{2} x^{4} c b + \frac {1}{3} x^{3} b^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{5} \, c^{2} x^{5} + \frac {1}{2} \, b c x^{4} + \frac {1}{3} \, b^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 25, normalized size = 0.83 \begin {gather*} \frac {1}{5} c^{2} x^{5}+\frac {1}{2} b c \,x^{4}+\frac {1}{3} b^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.30, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{5} \, c^{2} x^{5} + \frac {1}{2} \, b c x^{4} + \frac {1}{3} \, b^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {b^2\,x^3}{3}+\frac {b\,c\,x^4}{2}+\frac {c^2\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 24, normalized size = 0.80 \begin {gather*} \frac {b^{2} x^{3}}{3} + \frac {b c x^{4}}{2} + \frac {c^{2} x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________