3.2.70 \(\int \frac {\sin (a+b (c+d x)^2)}{(e+f x)^2} \, dx\) [170]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\sin \left (a+b (c+d x)^2\right )}{(e+f x)^2},x\right ) \]

[Out]

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

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 13.75, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sin \left (a+b (c+d x)^2\right )}{(e+f x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\sin \left (a +b \left (d x +c \right )^{2}\right )}{\left (f x +e \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+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 + a)/(f^2*x^2 + 2*f*x*e + e^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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