3.185 \(\int \frac{\sin (a+\frac{b}{(c+d x)^3})}{e+f x} \, dx\)

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

[Out]

Unintegrable[Sin[a + b/(c + d*x)^3]/(e + f*x), x]

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Rubi [A]  time = 0.0132455, 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 = {} \[ \int \frac{\sin \left (a+\frac{b}{(c+d x)^3}\right )}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sin[a + b/(c + d*x)^3]/(e + f*x),x]

[Out]

Defer[Int][Sin[a + b/(c + d*x)^3]/(e + f*x), x]

Rubi steps

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

Mathematica [A]  time = 5.15019, size = 0, normalized size = 0. \[ \int \frac{\sin \left (a+\frac{b}{(c+d x)^3}\right )}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x),x]

[Out]

Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x), x]

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Maple [A]  time = 0.273, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{fx+e}\sin \left ( a+{\frac{b}{ \left ( dx+c \right ) ^{3}}} \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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