3.102 \(\int \frac{f^{a+b x^3}}{x} \, dx\)

Optimal. Leaf size=15 \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]

[Out]

(f^a*ExpIntegralEi[b*x^3*Log[f]])/3

_______________________________________________________________________________________

Rubi [A]  time = 0.0344289, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]

Antiderivative was successfully verified.

[In]  Int[f^(a + b*x^3)/x,x]

[Out]

(f^a*ExpIntegralEi[b*x^3*Log[f]])/3

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 3.05968, size = 14, normalized size = 0.93 \[ \frac{f^{a} \operatorname{Ei}{\left (b x^{3} \log{\left (f \right )} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(f**(b*x**3+a)/x,x)

[Out]

f**a*Ei(b*x**3*log(f))/3

_______________________________________________________________________________________

Mathematica [A]  time = 0.0045556, size = 15, normalized size = 1. \[ \frac{1}{3} f^a \text{ExpIntegralEi}\left (b x^3 \log (f)\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[f^(a + b*x^3)/x,x]

[Out]

(f^a*ExpIntegralEi[b*x^3*Log[f]])/3

_______________________________________________________________________________________

Maple [B]  time = 0.022, size = 41, normalized size = 2.7 \[{\frac{{f}^{a} \left ( 3\,\ln \left ( x \right ) +\ln \left ( -b \right ) +\ln \left ( \ln \left ( f \right ) \right ) -\ln \left ( -b{x}^{3}\ln \left ( f \right ) \right ) -{\it Ei} \left ( 1,-b{x}^{3}\ln \left ( f \right ) \right ) \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f^(b*x^3+a)/x,x)

[Out]

1/3*f^a*(3*ln(x)+ln(-b)+ln(ln(f))-ln(-b*x^3*ln(f))-Ei(1,-b*x^3*ln(f)))

_______________________________________________________________________________________

Maxima [A]  time = 0.958367, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, f^{a}{\rm Ei}\left (b x^{3} \log \left (f\right )\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(b*x^3 + a)/x,x, algorithm="maxima")

[Out]

1/3*f^a*Ei(b*x^3*log(f))

_______________________________________________________________________________________

Fricas [A]  time = 0.269873, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, f^{a}{\rm Ei}\left (b x^{3} \log \left (f\right )\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(b*x^3 + a)/x,x, algorithm="fricas")

[Out]

1/3*f^a*Ei(b*x^3*log(f))

_______________________________________________________________________________________

Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + b x^{3}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f**(b*x**3+a)/x,x)

[Out]

Integral(f**(a + b*x**3)/x, x)

_______________________________________________________________________________________

GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{b x^{3} + a}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(b*x^3 + a)/x,x, algorithm="giac")

[Out]

integrate(f^(b*x^3 + a)/x, x)