Optimal. Leaf size=10 \[ -\frac {1}{x (a+b)} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {6, 12, 30} \begin {gather*} -\frac {1}{x (a+b)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{a x^2+b x^2} \, dx &=\int \frac {1}{(a+b) x^2} \, dx\\ &=\frac {\int \frac {1}{x^2} \, dx}{a+b}\\ &=-\frac {1}{(a+b) x}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{x (a+b)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{a x^2+b x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.37, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{{\left (a + b\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{{\left (a + b\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 11, normalized size = 1.10 \begin {gather*} -\frac {1}{\left (a +b \right ) x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.36, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{{\left (a + b\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{x\,\left (a+b\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 7, normalized size = 0.70 \begin {gather*} - \frac {1}{x \left (a + b\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________