Optimal. Leaf size=12 \[ b x+\frac {c x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 12, 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 = {14}
\begin {gather*} b x+\frac {c x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^2} \, dx &=\int \left (b+c x^2\right ) \, dx\\ &=b x+\frac {c x^3}{3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} b x+\frac {c x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 11, normalized size = 0.92
method | result | size |
default | \(b x +\frac {1}{3} c \,x^{3}\) | \(11\) |
risch | \(b x +\frac {1}{3} c \,x^{3}\) | \(11\) |
gosper | \(\frac {x \left (c \,x^{2}+3 b \right )}{3}\) | \(13\) |
norman | \(\frac {b \,x^{2}+\frac {1}{3} c \,x^{4}}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, c x^{3} + b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.32, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, c x^{3} + b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 8, normalized size = 0.67 \begin {gather*} b x + \frac {c x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.61, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, c x^{3} + b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} \frac {c\,x^3}{3}+b\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________