3.13.24 \(\int \frac {-1+74 x-250 x^2}{x} \, dx\)

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

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.52, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \begin {gather*} -125 x^2+74 x-\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 + 74*x - 250*x^2)/x,x]

[Out]

74*x - 125*x^2 - Log[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 {1}{x}-250 x\right ) \, dx\\ &=74 x-125 x^2-\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.52 \begin {gather*} 74 x-125 x^2-\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 + 74*x - 250*x^2)/x,x]

[Out]

74*x - 125*x^2 - Log[x]

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fricas [A]  time = 0.90, size = 13, normalized size = 0.52 \begin {gather*} -125 \, x^{2} + 74 \, x - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-250*x^2+74*x-1)/x,x, algorithm="fricas")

[Out]

-125*x^2 + 74*x - log(x)

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giac [A]  time = 0.28, size = 14, normalized size = 0.56 \begin {gather*} -125 \, x^{2} + 74 \, x - \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-250*x^2+74*x-1)/x,x, algorithm="giac")

[Out]

-125*x^2 + 74*x - log(abs(x))

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maple [A]  time = 0.01, size = 14, normalized size = 0.56

method	result	size
default	\(-125 x^{2}+74 x -\ln \relax (x )\)	\(14\)
norman	\(-125 x^{2}+74 x -\ln \relax (x )\)	\(14\)
risch	\(-125 x^{2}+74 x -\ln \relax (x )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-250*x^2+74*x-1)/x,x,method=_RETURNVERBOSE)

[Out]

-125*x^2+74*x-ln(x)

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maxima [A]  time = 0.41, size = 13, normalized size = 0.52 \begin {gather*} -125 \, x^{2} + 74 \, x - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-250*x^2+74*x-1)/x,x, algorithm="maxima")

[Out]

-125*x^2 + 74*x - log(x)

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mupad [B]  time = 0.85, size = 13, normalized size = 0.52 \begin {gather*} 74\,x-\ln \relax (x)-125\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(250*x^2 - 74*x + 1)/x,x)

[Out]

74*x - log(x) - 125*x^2

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sympy [A]  time = 0.07, size = 10, normalized size = 0.40 \begin {gather*} - 125 x^{2} + 74 x - \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-250*x**2+74*x-1)/x,x)

[Out]

-125*x**2 + 74*x - log(x)

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