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

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\sin \left (a+\frac {b}{(c+d x)^3}\right )}{e+f x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {\sin \left (a+\frac {b}{(c+d x)^3}\right )}{e+f x} \, dx \]

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*}

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Mathematica [A]  time = 5.15, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a+\frac {b}{(c+d x)^3}\right )}{e+f x} \, dx \]

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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fricas [A]  time = 0.82, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (\frac {a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right )}{f x + e}, x\right ) \]

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

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)

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maple [A]  time = 0.40, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a +\frac {b}{\left (d x +c \right )^{3}}\right )}{f x +e}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a + \frac {b}{{\left (d x + c\right )}^{3}}\right )}{f x + e}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\sin \left (a+\frac {b}{{\left (c+d\,x\right )}^3}\right )}{e+f\,x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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