Optimal. Leaf size=15 \[ -\frac {1}{x}+\frac {x^2}{2}+\log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14}
\begin {gather*} \frac {x^2}{2}-\frac {1}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {1+x+x^3}{x^2} \, dx &=\int \left (\frac {1}{x^2}+\frac {1}{x}+x\right ) \, dx\\ &=-\frac {1}{x}+\frac {x^2}{2}+\log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{x}+\frac {x^2}{2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 14, normalized size = 0.93
method | result | size |
default | \(-\frac {1}{x}+\frac {x^{2}}{2}+\ln \left (x \right )\) | \(14\) |
risch | \(-\frac {1}{x}+\frac {x^{2}}{2}+\ln \left (x \right )\) | \(14\) |
norman | \(\frac {-1+\frac {x^{3}}{2}}{x}+\ln \left (x \right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^{3} + 2 \, x \log \left (x\right ) - 2}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} \frac {x^{2}}{2} + \log {\left (x \right )} - \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.18, size = 14, normalized size = 0.93 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{x} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 13, normalized size = 0.87 \begin {gather*} \ln \left (x\right )-\frac {1}{x}+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________