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

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

[Out]

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

Verification is Not applicable to the result.

[In]

Int[Sin[b*(c + d*x)^2]/(e + f*x),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 5.32, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (b (c+d x)^2\right )}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.71, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )}{f x + e}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (\left (d x +c \right )^{2} b \right )}{f x +e}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(b*(c + d*x)^2)/(e + f*x),x)

[Out]

int(sin(b*(c + d*x)^2)/(e + f*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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