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

Optimal. Leaf size=17 \[ \text{Unintegrable}\left (\frac{f^{c (a+b x)^3}}{x},x\right ) \]

[Out]

Unintegrable[f^(c*(a + b*x)^3)/x, x]

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Rubi [A]  time = 0.0168283, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{f^{c (a+b x)^3}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c*(a + b*x)^3)/x,x]

[Out]

Defer[Int][f^(c*(a + b*x)^3)/x, x]

Rubi steps

\begin{align*} \int \frac{f^{c (a+b x)^3}}{x} \, dx &=\int \frac{f^{c (a+b x)^3}}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.295997, size = 0, normalized size = 0. \[ \int \frac{f^{c (a+b x)^3}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c*(a + b*x)^3)/x,x]

[Out]

Integrate[f^(c*(a + b*x)^3)/x, x]

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Maple [A]  time = 0.016, size = 0, normalized size = 0. \begin{align*} \int{\frac{{f}^{c \left ( bx+a \right ) ^{3}}}{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*(b*x+a)^3)/x,x)

[Out]

int(f^(c*(b*x+a)^3)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{{\left (b x + a\right )}^{3} c}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^3*c)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{f^{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(f^(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{c \left (a + b x\right )^{3}}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f**(c*(b*x+a)**3)/x,x)

[Out]

Integral(f**(c*(a + b*x)**3)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{{\left (b x + a\right )}^{3} c}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^3*c)/x, x)