3.3.53 \(\int \frac {f^{c (a+b x)^n}}{x^3} \, dx\) [253]

Optimal. Leaf size=18 \[ \text {Int}\left (\frac {f^{c (a+b x)^n}}{x^3},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.03, 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 {f^{c (a+b x)^n}}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[f^(c*(a + b*x)^n)/x^3,x]

[Out]

Defer[Int][f^(c*(a + b*x)^n)/x^3, x]

Rubi steps

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

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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{c (a+b x)^n}}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[f^(c*(a + b*x)^n)/x^3,x]

[Out]

Integrate[f^(c*(a + b*x)^n)/x^3, x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {f^{c \left (b x +a \right )^{n}}}{x^{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^n*c)/x^3, x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(f^((b*x + a)^n*c)/x^3, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{c \left (a + b x\right )^{n}}}{x^{3}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c*(a + b*x)**n)/x**3, x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^n*c)/x^3, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {f^{c\,{\left (a+b\,x\right )}^n}}{x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*(a + b*x)^n)/x^3,x)

[Out]

int(f^(c*(a + b*x)^n)/x^3, x)

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