Optimal. Leaf size=21 \[ -\frac {2+3 x}{2 \left (4+7 x+2 x^2\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {1674, 8}
\begin {gather*} -\frac {3 x+2}{2 \left (2 x^2+7 x+4\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rule 1674
Rubi steps
\begin {align*} \int \frac {1+4 x+3 x^2}{\left (4+7 x+2 x^2\right )^2} \, dx &=-\frac {2+3 x}{2 \left (4+7 x+2 x^2\right )}-\frac {\int 0 \, dx}{17}\\ &=-\frac {2+3 x}{2 \left (4+7 x+2 x^2\right )}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {-2-3 x}{2 \left (4+7 x+2 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 17, normalized size = 0.81
method | result | size |
default | \(\frac {-\frac {3 x}{4}-\frac {1}{2}}{x^{2}+\frac {7}{2} x +2}\) | \(17\) |
risch | \(\frac {-\frac {3 x}{4}-\frac {1}{2}}{x^{2}+\frac {7}{2} x +2}\) | \(17\) |
norman | \(\frac {-\frac {3 x}{2}-1}{2 x^{2}+7 x +4}\) | \(19\) |
gosper | \(-\frac {2+3 x}{2 \left (2 x^{2}+7 x +4\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 19, normalized size = 0.90 \begin {gather*} -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 19, normalized size = 0.90 \begin {gather*} -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 15, normalized size = 0.71 \begin {gather*} \frac {- 3 x - 2}{4 x^{2} + 14 x + 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.81, size = 19, normalized size = 0.90 \begin {gather*} -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.84, size = 17, normalized size = 0.81 \begin {gather*} -\frac {\frac {3\,x}{4}+\frac {1}{2}}{x^2+\frac {7\,x}{2}+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________