3.28.79 \(\int \frac {-3-147 x-75 x^2+(-147 x-150 x^2) \log (2 x)}{(5 x+490 x^2+12255 x^3+12250 x^4+3125 x^5) \log ^2(2 x)} \, dx\)

Optimal. Leaf size=23 \[ \frac {3}{5 (1-x+25 x (2+x)) \log (2 x)} \]

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Rubi [F]  time = 0.60, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-3-147 x-75 x^2+\left (-147 x-150 x^2\right ) \log (2 x)}{\left (5 x+490 x^2+12255 x^3+12250 x^4+3125 x^5\right ) \log ^2(2 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-3 - 147*x - 75*x^2 + (-147*x - 150*x^2)*Log[2*x])/((5*x + 490*x^2 + 12255*x^3 + 12250*x^4 + 3125*x^5)*Lo
g[2*x]^2),x]

[Out]

(-3*Defer[Int][1/(x*(1 + 49*x + 25*x^2)*Log[2*x]^2), x])/5 - (3*Defer[Int][(49 + 50*x)/((1 + 49*x + 25*x^2)^2*
Log[2*x]), x])/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3-147 x-75 x^2+\left (-147 x-150 x^2\right ) \log (2 x)}{5 x \left (1+49 x+25 x^2\right )^2 \log ^2(2 x)} \, dx\\ &=\frac {1}{5} \int \frac {-3-147 x-75 x^2+\left (-147 x-150 x^2\right ) \log (2 x)}{x \left (1+49 x+25 x^2\right )^2 \log ^2(2 x)} \, dx\\ &=\frac {1}{5} \int \left (-\frac {3}{x \left (1+49 x+25 x^2\right ) \log ^2(2 x)}-\frac {3 (49+50 x)}{\left (1+49 x+25 x^2\right )^2 \log (2 x)}\right ) \, dx\\ &=-\left (\frac {3}{5} \int \frac {1}{x \left (1+49 x+25 x^2\right ) \log ^2(2 x)} \, dx\right )-\frac {3}{5} \int \frac {49+50 x}{\left (1+49 x+25 x^2\right )^2 \log (2 x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 22, normalized size = 0.96 \begin {gather*} -\frac {3}{5 \left (-1-49 x-25 x^2\right ) \log (2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3 - 147*x - 75*x^2 + (-147*x - 150*x^2)*Log[2*x])/((5*x + 490*x^2 + 12255*x^3 + 12250*x^4 + 3125*x
^5)*Log[2*x]^2),x]

[Out]

-3/(5*(-1 - 49*x - 25*x^2)*Log[2*x])

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fricas [A]  time = 0.49, size = 20, normalized size = 0.87 \begin {gather*} \frac {3}{5 \, {\left (25 \, x^{2} + 49 \, x + 1\right )} \log \left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-150*x^2-147*x)*log(2*x)-75*x^2-147*x-3)/(3125*x^5+12250*x^4+12255*x^3+490*x^2+5*x)/log(2*x)^2,x,
algorithm="fricas")

[Out]

3/5/((25*x^2 + 49*x + 1)*log(2*x))

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giac [A]  time = 0.22, size = 25, normalized size = 1.09 \begin {gather*} \frac {3}{5 \, {\left (25 \, x^{2} \log \left (2 \, x\right ) + 49 \, x \log \left (2 \, x\right ) + \log \left (2 \, x\right )\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-150*x^2-147*x)*log(2*x)-75*x^2-147*x-3)/(3125*x^5+12250*x^4+12255*x^3+490*x^2+5*x)/log(2*x)^2,x,
algorithm="giac")

[Out]

3/5/(25*x^2*log(2*x) + 49*x*log(2*x) + log(2*x))

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maple [A]  time = 0.08, size = 21, normalized size = 0.91

method	result	size
norman	\(\frac {3}{5 \left (25 x^{2}+49 x +1\right ) \ln \left (2 x \right )}\)	\(21\)
risch	\(\frac {3}{5 \left (25 x^{2}+49 x +1\right ) \ln \left (2 x \right )}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-150*x^2-147*x)*ln(2*x)-75*x^2-147*x-3)/(3125*x^5+12250*x^4+12255*x^3+490*x^2+5*x)/ln(2*x)^2,x,method=_R
ETURNVERBOSE)

[Out]

3/5/(25*x^2+49*x+1)/ln(2*x)

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maxima [A]  time = 0.77, size = 32, normalized size = 1.39 \begin {gather*} \frac {3}{5 \, {\left (25 \, x^{2} \log \relax (2) + 49 \, x \log \relax (2) + {\left (25 \, x^{2} + 49 \, x + 1\right )} \log \relax (x) + \log \relax (2)\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-150*x^2-147*x)*log(2*x)-75*x^2-147*x-3)/(3125*x^5+12250*x^4+12255*x^3+490*x^2+5*x)/log(2*x)^2,x,
algorithm="maxima")

[Out]

3/5/(25*x^2*log(2) + 49*x*log(2) + (25*x^2 + 49*x + 1)*log(x) + log(2))

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mupad [B]  time = 2.12, size = 20, normalized size = 0.87 \begin {gather*} \frac {3}{5\,\ln \left (2\,x\right )\,\left (25\,x^2+49\,x+1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(147*x + log(2*x)*(147*x + 150*x^2) + 75*x^2 + 3)/(log(2*x)^2*(5*x + 490*x^2 + 12255*x^3 + 12250*x^4 + 31
25*x^5)),x)

[Out]

3/(5*log(2*x)*(49*x + 25*x^2 + 1))

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sympy [A]  time = 0.14, size = 15, normalized size = 0.65 \begin {gather*} \frac {3}{\left (125 x^{2} + 245 x + 5\right ) \log {\left (2 x \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-150*x**2-147*x)*ln(2*x)-75*x**2-147*x-3)/(3125*x**5+12250*x**4+12255*x**3+490*x**2+5*x)/ln(2*x)**
2,x)

[Out]

3/((125*x**2 + 245*x + 5)*log(2*x))

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