3.3.4 \(\int \frac {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\) [204]

Optimal. Leaf size=34 \[ \text {Int}\left (\frac {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]

[Out]

Unintegrable(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x)

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Rubi [A]
time = 0.06, 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 {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]

[Out]

Defer[Int][Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]

Rubi steps

\begin {align*} \int \frac {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end {align*}

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Mathematica [A]
time = 161.13, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]

[Out]

Integrate[Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\sinh ^{3}\left (d x +c \right )}{\left (f x +e \right )^{2} \left (a +i a \sinh \left (d x +c \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x)

[Out]

int(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x)

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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.

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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(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="fricas")

[Out]

((-I*a*d*f^2*x^2 - 2*I*a*d*f*x*e - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*f*x*e + a*d*e^2)*e^(d*x + c))*integral(-1/
4*(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(5*d*x + 5*c) - (d*f*x + d*e)*e^(4*d*x + 4*c) + 4*(-I*d*f*x - I*d*e)*e^(
3*d*x + 3*c) - 4*(d*f*x + d*e + 4*f)*e^(2*d*x + 2*c) - (I*d*f*x + I*d*e)*e^(d*x + c))/((a*d*f^3*x^3 + 3*a*d*f^
2*x^2*e + 3*a*d*f*x*e^2 + a*d*e^3)*e^(3*d*x + 3*c) - (I*a*d*f^3*x^3 + 3*I*a*d*f^2*x^2*e + 3*I*a*d*f*x*e^2 + I*
a*d*e^3)*e^(2*d*x + 2*c)), x) + 2)/(-I*a*d*f^2*x^2 - 2*I*a*d*f*x*e - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*f*x*e +
a*d*e^2)*e^(d*x + c))

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sinh(d*x+c)**3/(f*x+e)**2/(a+I*a*sinh(d*x+c)),x)

[Out]

Timed out

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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(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="giac")

[Out]

integrate(sinh(d*x + c)^3/((f*x + e)^2*(I*a*sinh(d*x + c) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {sinh}\left (c+d\,x\right )}^3}{{\left (e+f\,x\right )}^2\,\left (a+a\,\mathrm {sinh}\left (c+d\,x\right )\,1{}\mathrm {i}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinh(c + d*x)^3/((e + f*x)^2*(a + a*sinh(c + d*x)*1i)),x)

[Out]

int(sinh(c + d*x)^3/((e + f*x)^2*(a + a*sinh(c + d*x)*1i)), x)

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