3.60.34 \(\int \frac {1875-74 x^2}{x^2} \, dx\)

Optimal. Leaf size=20 \[ 5+x-3 \left (\frac {1}{e^4}+\frac {(-25+5 x)^2}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.45, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} -74 x-\frac {1875}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1875 - 74*x^2)/x^2,x]

[Out]

-1875/x - 74*x

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-74+\frac {1875}{x^2}\right ) \, dx\\ &=-\frac {1875}{x}-74 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.45 \begin {gather*} -\frac {1875}{x}-74 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1875 - 74*x^2)/x^2,x]

[Out]

-1875/x - 74*x

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fricas [A]  time = 0.67, size = 12, normalized size = 0.60 \begin {gather*} -\frac {74 \, x^{2} + 1875}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-74*x^2+1875)/x^2,x, algorithm="fricas")

[Out]

-(74*x^2 + 1875)/x

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giac [A]  time = 0.11, size = 9, normalized size = 0.45 \begin {gather*} -74 \, x - \frac {1875}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-74*x^2+1875)/x^2,x, algorithm="giac")

[Out]

-74*x - 1875/x

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maple [A]  time = 0.03, size = 10, normalized size = 0.50

method	result	size
default	\(-74 x -\frac {1875}{x}\)	\(10\)
risch	\(-74 x -\frac {1875}{x}\)	\(10\)
norman	\(\frac {-74 x^{2}-1875}{x}\)	\(12\)
gosper	\(-\frac {74 x^{2}+1875}{x}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-74*x^2+1875)/x^2,x,method=_RETURNVERBOSE)

[Out]

-74*x-1875/x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.45 \begin {gather*} -74 \, x - \frac {1875}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-74*x^2+1875)/x^2,x, algorithm="maxima")

[Out]

-74*x - 1875/x

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mupad [B]  time = 0.03, size = 9, normalized size = 0.45 \begin {gather*} -74\,x-\frac {1875}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(74*x^2 - 1875)/x^2,x)

[Out]

- 74*x - 1875/x

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sympy [A]  time = 0.06, size = 7, normalized size = 0.35 \begin {gather*} - 74 x - \frac {1875}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-74*x**2+1875)/x**2,x)

[Out]

-74*x - 1875/x

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