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

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

[Out]

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

________________________________________________________________________________________

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

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

________________________________________________________________________________________

Mathematica [A]  time = 21.10, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.63, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left ({\left (d x + c\right )}^{\frac {2}{3}} b + a\right )}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right ) \]

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

________________________________________________________________________________________

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

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

________________________________________________________________________________________

maple [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a +b \left (d x +c \right )^{\frac {2}{3}}\right )}{\left (f x +e \right )^{2}}\, dx \]

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)

________________________________________________________________________________________

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

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

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________