3.52.7 \(\int \frac {3 x^3+(30-30 x) \log (3) \log (25)}{x^3} \, dx\)

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

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {14} \begin {gather*} -\frac {15 \log (3) \log (25)}{x^2}+3 x+\frac {30 \log (3) \log (25)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3*x^3 + (30 - 30*x)*Log[3]*Log[25])/x^3,x]

[Out]

3*x - (15*Log[3]*Log[25])/x^2 + (30*Log[3]*Log[25])/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 (3+\frac {30 \log (3) \log (25)}{x^3}-\frac {30 \log (3) \log (25)}{x^2}\right ) \, dx\\ &=3 x-\frac {15 \log (3) \log (25)}{x^2}+\frac {30 \log (3) \log (25)}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 22, normalized size = 1.10 \begin {gather*} 3 x-\frac {15 \log (3) \log (25)}{x^2}+\frac {30 \log (3) \log (25)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*x^3 + (30 - 30*x)*Log[3]*Log[25])/x^3,x]

[Out]

3*x - (15*Log[3]*Log[25])/x^2 + (30*Log[3]*Log[25])/x

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fricas [A]  time = 0.55, size = 20, normalized size = 1.00 \begin {gather*} \frac {3 \, {\left (x^{3} + 10 \, {\left (2 \, x - 1\right )} \log \relax (5) \log \relax (3)\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-30*x+30)*log(3)*log(5)+3*x^3)/x^3,x, algorithm="fricas")

[Out]

3*(x^3 + 10*(2*x - 1)*log(5)*log(3))/x^2

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giac [A]  time = 0.14, size = 23, normalized size = 1.15 \begin {gather*} 3 \, x + \frac {30 \, {\left (2 \, x \log \relax (5) \log \relax (3) - \log \relax (5) \log \relax (3)\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-30*x+30)*log(3)*log(5)+3*x^3)/x^3,x, algorithm="giac")

[Out]

3*x + 30*(2*x*log(5)*log(3) - log(5)*log(3))/x^2

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maple [A]  time = 0.05, size = 23, normalized size = 1.15

method	result	size
gosper	\(\frac {3 x^{3}-30 \ln \relax (3) \ln \relax (5)+60 x \ln \relax (3) \ln \relax (5)}{x^{2}}\)	\(23\)
default	\(3 x +\frac {60 \ln \relax (3) \ln \relax (5)}{x}-\frac {30 \ln \relax (3) \ln \relax (5)}{x^{2}}\)	\(23\)
risch	\(3 x +\frac {60 x \ln \relax (3) \ln \relax (5)-30 \ln \relax (3) \ln \relax (5)}{x^{2}}\)	\(23\)
norman	\(\frac {3 x^{3}-30 \ln \relax (3) \ln \relax (5)+60 x \ln \relax (3) \ln \relax (5)}{x^{2}}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*(-30*x+30)*ln(3)*ln(5)+3*x^3)/x^3,x,method=_RETURNVERBOSE)

[Out]

3*(20*x*ln(3)*ln(5)+x^3-10*ln(3)*ln(5))/x^2

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maxima [A]  time = 0.34, size = 23, normalized size = 1.15 \begin {gather*} 3 \, x + \frac {30 \, {\left (2 \, x \log \relax (5) \log \relax (3) - \log \relax (5) \log \relax (3)\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-30*x+30)*log(3)*log(5)+3*x^3)/x^3,x, algorithm="maxima")

[Out]

3*x + 30*(2*x*log(5)*log(3) - log(5)*log(3))/x^2

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mupad [B]  time = 0.04, size = 23, normalized size = 1.15 \begin {gather*} 3\,x-\frac {30\,\ln \relax (3)\,\ln \relax (5)-60\,x\,\ln \relax (3)\,\ln \relax (5)}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x^3 - 2*log(3)*log(5)*(30*x - 30))/x^3,x)

[Out]

3*x - (30*log(3)*log(5) - 60*x*log(3)*log(5))/x^2

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sympy [A]  time = 0.11, size = 24, normalized size = 1.20 \begin {gather*} 3 x + \frac {60 x \log {\relax (3 )} \log {\relax (5 )} - 30 \log {\relax (3 )} \log {\relax (5 )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(-30*x+30)*ln(3)*ln(5)+3*x**3)/x**3,x)

[Out]

3*x + (60*x*log(3)*log(5) - 30*log(3)*log(5))/x**2

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