3.226 \(\int \frac {\sin (a+\frac {b}{(c+d x)^{2/3}})}{(e+f x)^2} \, dx\)

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\sin \left (a+\frac {b}{(c+d x)^{2/3}}\right )}{(e+f x)^2},x\right ) \]

[Out]

Unintegrable(sin(a+b/(d*x+c)^(2/3))/(f*x+e)^2,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 = {} \[ \int \frac {\sin \left (a+\frac {b}{(c+d x)^{2/3}}\right )}{(e+f x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {align*} \int \frac {\sin \left (a+\frac {b}{(c+d x)^{2/3}}\right )}{(e+f x)^2} \, dx &=\int \frac {\sin \left (a+\frac {b}{(c+d x)^{2/3}}\right )}{(e+f x)^2} \, dx\\ \end {align*}

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Mathematica [F]  time = 180.03, size = 0, normalized size = 0.00 \[ \text {\$Aborted} \]

Verification is Not applicable to the result.

[In]

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

[Out]

$Aborted

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fricas [A]  time = 0.69, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (\frac {a d x + a c + {\left (d x + c\right )}^{\frac {1}{3}} b}{d x + c}\right )}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(f^2*x^2 + 2*e*f*x + e^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+b/(d*x+c)^(2/3))/(f*x+e)^2,x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {2}{3}}}\right )}{\left (f x +e \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\sin \left (a+\frac {b}{{\left (c+d\,x\right )}^{2/3}}\right )}{{\left (e+f\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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