3.278 \(\int \frac{4+3 x^4}{5 x+2 x^5} \, dx\)

Optimal. Leaf size=19 \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]

[Out]

(4*Log[x])/5 + (7*Log[5 + 2*x^4])/40

_______________________________________________________________________________________

Rubi [A]  time = 0.0543293, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]

Antiderivative was successfully verified.

[In]  Int[(4 + 3*x^4)/(5*x + 2*x^5),x]

[Out]

(4*Log[x])/5 + (7*Log[5 + 2*x^4])/40

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.28586, size = 17, normalized size = 0.89 \[ \frac{\log{\left (x^{4} \right )}}{5} + \frac{7 \log{\left (2 x^{4} + 5 \right )}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3*x**4+4)/(2*x**5+5*x),x)

[Out]

log(x**4)/5 + 7*log(2*x**4 + 5)/40

_______________________________________________________________________________________

Mathematica [A]  time = 0.008972, size = 19, normalized size = 1. \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[(4 + 3*x^4)/(5*x + 2*x^5),x]

[Out]

(4*Log[x])/5 + (7*Log[5 + 2*x^4])/40

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 16, normalized size = 0.8 \[{\frac{4\,\ln \left ( x \right ) }{5}}+{\frac{7\,\ln \left ( 2\,{x}^{4}+5 \right ) }{40}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3*x^4+4)/(2*x^5+5*x),x)

[Out]

4/5*ln(x)+7/40*ln(2*x^4+5)

_______________________________________________________________________________________

Maxima [A]  time = 1.51112, size = 20, normalized size = 1.05 \[ \frac{7}{40} \, \log \left (2 \, x^{4} + 5\right ) + \frac{4}{5} \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="maxima")

[Out]

7/40*log(2*x^4 + 5) + 4/5*log(x)

_______________________________________________________________________________________

Fricas [A]  time = 0.206577, size = 20, normalized size = 1.05 \[ \frac{7}{40} \, \log \left (2 \, x^{4} + 5\right ) + \frac{4}{5} \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="fricas")

[Out]

7/40*log(2*x^4 + 5) + 4/5*log(x)

_______________________________________________________________________________________

Sympy [A]  time = 0.108864, size = 17, normalized size = 0.89 \[ \frac{4 \log{\left (x \right )}}{5} + \frac{7 \log{\left (2 x^{4} + 5 \right )}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x**4+4)/(2*x**5+5*x),x)

[Out]

4*log(x)/5 + 7*log(2*x**4 + 5)/40

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.224476, size = 23, normalized size = 1.21 \[ \frac{7}{40} \,{\rm ln}\left (2 \, x^{4} + 5\right ) + \frac{1}{5} \,{\rm ln}\left (x^{4}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="giac")

[Out]

7/40*ln(2*x^4 + 5) + 1/5*ln(x^4)