3.5.47 \(\int \frac {f^{a+b x+c x^2}}{d+e x} \, dx\) [447]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {f^{a+b x+c x^2}}{d+e x},x\right ) \]

[Out]

Unintegrable(f^(c*x^2+b*x+a)/(e*x+d),x)

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Rubi [A]
time = 0.02, 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^{a+b x+c x^2}}{d+e x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[f^(a + b*x + c*x^2)/(d + e*x),x]

[Out]

Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x]

Rubi steps

\begin {align*} \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx &=\int \frac {f^{a+b x+c x^2}}{d+e x} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[f^(a + b*x + c*x^2)/(d + e*x),x]

[Out]

Integrate[f^(a + b*x + c*x^2)/(d + e*x), x]

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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {f^{c \,x^{2}+b x +a}}{e x +d}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*x^2+b*x+a)/(e*x+d),x)

[Out]

int(f^(c*x^2+b*x+a)/(e*x+d),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*x^2+b*x+a)/(e*x+d),x, algorithm="maxima")

[Out]

integrate(f^(c*x^2 + b*x + a)/(e*x + d), 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*x^2+b*x+a)/(e*x+d),x, algorithm="fricas")

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{a + b x + c x^{2}}}{d + e x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f**(c*x**2+b*x+a)/(e*x+d),x)

[Out]

Integral(f**(a + b*x + c*x**2)/(d + e*x), 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*x^2+b*x+a)/(e*x+d),x, algorithm="giac")

[Out]

integrate(f^(c*x^2 + b*x + a)/(x*e + d), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {f^{c\,x^2+b\,x+a}}{d+e\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(a + b*x + c*x^2)/(d + e*x),x)

[Out]

int(f^(a + b*x + c*x^2)/(d + e*x), x)

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