3.1810 \(\int (a+\frac{b}{x^2}) \, dx\)

Optimal. Leaf size=10 \[ a x-\frac{b}{x} \]

[Out]

-(b/x) + a*x

________________________________________________________________________________________

Rubi [A]  time = 0.0021625, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]

Int[a + b/x^2,x]

[Out]

-(b/x) + a*x

Rubi steps

\begin{align*} \int \left (a+\frac{b}{x^2}\right ) \, dx &=-\frac{b}{x}+a x\\ \end{align*}

Mathematica [A]  time = 0.0001771, size = 10, normalized size = 1. \[ a x-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b/x^2,x]

[Out]

-(b/x) + a*x

________________________________________________________________________________________

Maple [A]  time = 0.001, size = 11, normalized size = 1.1 \begin{align*} -{\frac{b}{x}}+ax \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a+1/x^2*b,x)

[Out]

-b/x+a*x

________________________________________________________________________________________

Maxima [A]  time = 0.987496, size = 14, normalized size = 1.4 \begin{align*} a x - \frac{b}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^2,x, algorithm="maxima")

[Out]

a*x - b/x

________________________________________________________________________________________

Fricas [A]  time = 1.39993, size = 20, normalized size = 2. \begin{align*} \frac{a x^{2} - b}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^2,x, algorithm="fricas")

[Out]

(a*x^2 - b)/x

________________________________________________________________________________________

Sympy [A]  time = 0.222163, size = 5, normalized size = 0.5 \begin{align*} a x - \frac{b}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x**2,x)

[Out]

a*x - b/x

________________________________________________________________________________________

Giac [A]  time = 1.15753, size = 14, normalized size = 1.4 \begin{align*} a x - \frac{b}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^2,x, algorithm="giac")

[Out]

a*x - b/x