3.158 \(\int \frac {\sin (b (c+d x)^2)}{(e+f x)^2} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {\sin \left (b (c+d x)^2\right )}{(e+f x)^2},x\right ) \]

[Out]

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

Verification is Not applicable to the result.

[In]

Int[Sin[b*(c + d*x)^2]/(e + f*x)^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 10.01, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (b (c+d x)^2\right )}{(e+f x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.83, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.28, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (\left (d x +c \right )^{2} b \right )}{\left (f x +e \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\sin \left (b\,{\left (c+d\,x\right )}^2\right )}{{\left (e+f\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(b*(c + d*x)^2)/(e + f*x)^2,x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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