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

Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\sin \left (a+\frac{b}{(c+d x)^{2/3}}\right )}{e+f x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.013414, 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 = {} \[ \int \frac{\sin \left (a+\frac{b}{(c+d x)^{2/3}}\right )}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 29.6677, size = 0, normalized size = 0. \[ \int \frac{\sin \left (a+\frac{b}{(c+d x)^{2/3}}\right )}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]  time = 0.058, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{fx+e}\sin \left ( a+{b \left ( dx+c \right ) ^{-{\frac{2}{3}}}} \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin \left (a + \frac{b}{{\left (d x + c\right )}^{\frac{2}{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)^(2/3))/(f*x+e),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\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 x + e}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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)**(2/3))/(f*x+e),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin \left (a + \frac{b}{{\left (d x + c\right )}^{\frac{2}{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)^(2/3))/(f*x+e),x, algorithm="giac")

[Out]

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