3.1.69 \(\int \frac {\sqrt {c+d x}}{(a+b e^x)^3} \, dx\) [69]

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {\sqrt {c+d x}}{\left (a+b e^x\right )^3},x\right ) \]

[Out]

Unintegrable((d*x+c)^(1/2)/(a+b*exp(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 {\sqrt {c+d x}}{\left (a+b e^x\right )^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sqrt[c + d*x]/(a + b*E^x)^3,x]

[Out]

Defer[Int][Sqrt[c + d*x]/(a + b*E^x)^3, x]

Rubi steps

\begin {align*} \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^3} \, dx &=\int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^3} \, dx\\ \end {align*}

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Mathematica [A]
time = 5.01, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sqrt[c + d*x]/(a + b*E^x)^3,x]

[Out]

Integrate[Sqrt[c + d*x]/(a + b*E^x)^3, x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^(1/2)/(a+b*exp(x))^3,x)

[Out]

int((d*x+c)^(1/2)/(a+b*exp(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((d*x+c)^(1/2)/(a+b*exp(x))^3,x, algorithm="maxima")

[Out]

integrate(sqrt(d*x + c)/(b*e^x + a)^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((d*x+c)^(1/2)/(a+b*exp(x))^3,x, algorithm="fricas")

[Out]

integral(sqrt(d*x + c)/(b^3*e^(3*x) + 3*a*b^2*e^(2*x) + 3*a^2*b*e^x + a^3), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**(1/2)/(a+b*exp(x))**3,x)

[Out]

Integral(sqrt(c + d*x)/(a + b*exp(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((d*x+c)^(1/2)/(a+b*exp(x))^3,x, algorithm="giac")

[Out]

integrate(sqrt(d*x + c)/(b*e^x + a)^3, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\sqrt {c+d\,x}}{{\left (a+b\,{\mathrm {e}}^x\right )}^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^(1/2)/(a + b*exp(x))^3,x)

[Out]

int((c + d*x)^(1/2)/(a + b*exp(x))^3, x)

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