3.4.91 \(\int \frac {7+2 x^2+e^{7 x+7 x \log (x)} (14 x^2+7 x^2 \log (x))}{x^2} \, dx\)

Optimal. Leaf size=26 \[ 3+e^{7 (x+x \log (x))}+\frac {1+2 (-4+x) (1+x)}{x} \]

________________________________________________________________________________________

Rubi [F]  time = 0.17, 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 {7+2 x^2+e^{7 x+7 x \log (x)} \left (14 x^2+7 x^2 \log (x)\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(7 + 2*x^2 + E^(7*x + 7*x*Log[x])*(14*x^2 + 7*x^2*Log[x]))/x^2,x]

[Out]

-7/x + 2*x + 14*Defer[Int][E^(7*x)*x^(7*x), x] + 7*Log[x]*Defer[Int][E^(7*x)*x^(7*x), x] - 7*Defer[Int][Defer[
Int][E^(7*x)*x^(7*x), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {7+2 x^2}{x^2}+7 e^{7 x} x^{7 x} (2+\log (x))\right ) \, dx\\ &=7 \int e^{7 x} x^{7 x} (2+\log (x)) \, dx+\int \frac {7+2 x^2}{x^2} \, dx\\ &=7 \int \left (2 e^{7 x} x^{7 x}+e^{7 x} x^{7 x} \log (x)\right ) \, dx+\int \left (2+\frac {7}{x^2}\right ) \, dx\\ &=-\frac {7}{x}+2 x+7 \int e^{7 x} x^{7 x} \log (x) \, dx+14 \int e^{7 x} x^{7 x} \, dx\\ &=-\frac {7}{x}+2 x-7 \int \frac {\int e^{7 x} x^{7 x} \, dx}{x} \, dx+14 \int e^{7 x} x^{7 x} \, dx+(7 \log (x)) \int e^{7 x} x^{7 x} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.07, size = 20, normalized size = 0.77 \begin {gather*} -\frac {7}{x}+2 x+e^{7 x} x^{7 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 + 2*x^2 + E^(7*x + 7*x*Log[x])*(14*x^2 + 7*x^2*Log[x]))/x^2,x]

[Out]

-7/x + 2*x + E^(7*x)*x^(7*x)

________________________________________________________________________________________

fricas [A]  time = 1.38, size = 23, normalized size = 0.88 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (7 \, x \log \relax (x) + 7 \, x\right )} - 7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7*x^2*log(x)+14*x^2)*exp(7*x*log(x)+7*x)+2*x^2+7)/x^2,x, algorithm="fricas")

[Out]

(2*x^2 + x*e^(7*x*log(x) + 7*x) - 7)/x

________________________________________________________________________________________

giac [A]  time = 0.26, size = 23, normalized size = 0.88 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (7 \, x \log \relax (x) + 7 \, x\right )} - 7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7*x^2*log(x)+14*x^2)*exp(7*x*log(x)+7*x)+2*x^2+7)/x^2,x, algorithm="giac")

[Out]

(2*x^2 + x*e^(7*x*log(x) + 7*x) - 7)/x

________________________________________________________________________________________

maple [A]  time = 0.07, size = 20, normalized size = 0.77

method	result	size
default	\({\mathrm e}^{7 x \ln \relax (x )+7 x}+2 x -\frac {7}{x}\)	\(20\)
risch	\(x^{7 x} {\mathrm e}^{7 x}+2 x -\frac {7}{x}\)	\(20\)
norman	\(\frac {-7+x \,{\mathrm e}^{7 x \ln \relax (x )+7 x}+2 x^{2}}{x}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((7*x^2*ln(x)+14*x^2)*exp(7*x*ln(x)+7*x)+2*x^2+7)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(7*x*ln(x)+7*x)+2*x-7/x

________________________________________________________________________________________

maxima [A]  time = 0.83, size = 19, normalized size = 0.73 \begin {gather*} 2 \, x - \frac {7}{x} + e^{\left (7 \, x \log \relax (x) + 7 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7*x^2*log(x)+14*x^2)*exp(7*x*log(x)+7*x)+2*x^2+7)/x^2,x, algorithm="maxima")

[Out]

2*x - 7/x + e^(7*x*log(x) + 7*x)

________________________________________________________________________________________

mupad [B]  time = 0.48, size = 19, normalized size = 0.73 \begin {gather*} 2\,x+x^{7\,x}\,{\mathrm {e}}^{7\,x}-\frac {7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(7*x + 7*x*log(x))*(7*x^2*log(x) + 14*x^2) + 2*x^2 + 7)/x^2,x)

[Out]

2*x + x^(7*x)*exp(7*x) - 7/x

________________________________________________________________________________________

sympy [A]  time = 0.27, size = 17, normalized size = 0.65 \begin {gather*} 2 x + e^{7 x \log {\relax (x )} + 7 x} - \frac {7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7*x**2*ln(x)+14*x**2)*exp(7*x*ln(x)+7*x)+2*x**2+7)/x**2,x)

[Out]

2*x + exp(7*x*log(x) + 7*x) - 7/x

________________________________________________________________________________________