3.3.25 \(\int -\sin (x-\sin (x)) \, dx\) [225]

Optimal. Leaf size=12 \[ -\text {Int}(\sin (x-\sin (x)),x) \]

[Out]

-CannotIntegrate(sin(x-sin(x)),x)

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Rubi [A]
time = 0.00, 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 -\sin (x-\sin (x)) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[-Sin[x - Sin[x]],x]

[Out]

-Defer[Int][Sin[x - Sin[x]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {Integral} &=-\int \sin (x-\sin (x)) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.80, size = 0, normalized size = 0.00 \begin {gather*} \int -\sin (x-\sin (x)) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[-Sin[x - Sin[x]],x]

[Out]

-Integrate[Sin[x - Sin[x]], x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int -\sin \left (x -\sin \left (x \right )\right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-sin(x-sin(x)),x)

[Out]

int(-sin(x-sin(x)),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(x-sin(x)),x, algorithm="maxima")

[Out]

integrate(sin(-x + sin(x)), x)

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Fricas [A]
time = 0.60, size = 9, normalized size = 0.75 \begin {gather*} {\rm integral}\left (\sin \left (-x + \sin \left (x\right )\right ), x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-sin(x-sin(x)),x, algorithm="fricas")

[Out]

integral(sin(-x + sin(x)), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \int \sin {\left (x - \sin {\left (x \right )} \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-sin(x-sin(x)),x)

[Out]

-Integral(sin(x - sin(x)), 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(x-sin(x)),x, algorithm="giac")

[Out]

integrate(-sin(x - sin(x)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int -\sin \left (x-\sin \left (x\right )\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-sin(x - sin(x)),x)

[Out]

int(-sin(x - sin(x)), x)

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Chatgpt [F] Failed to verify
time = 1.00, size = 11, normalized size = 0.92 \begin {gather*} -2 \cos \left (x -\sin \left (x \right )\right )+x \end {gather*}

Warning: Unable to verify antiderivative.

[In]

int(-sin(x-sin(x)),x)

[Out]

-2*cos(x-sin(x))+x

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