3.914 \(\int (10 x^9 \cos (x^5 \log (x))-x^{10} (x^4+5 x^4 \log (x)) \sin (x^5 \log (x))) \, dx\)

Optimal. Leaf size=11 \[ x^{10} \cos \left (x^5 \log (x)\right ) \]

[Out]

x^10*Cos[x^5*Log[x]]

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Rubi [F]  time = 0.275911, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \left (10 x^9 \cos \left (x^5 \log (x)\right )-x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right )\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[10*x^9*Cos[x^5*Log[x]] - x^10*(x^4 + 5*x^4*Log[x])*Sin[x^5*Log[x]],x]

[Out]

10*Defer[Int][x^9*Cos[x^5*Log[x]], x] - Defer[Int][x^14*Sin[x^5*Log[x]], x] - 5*Defer[Int][x^14*Log[x]*Sin[x^5
*Log[x]], x]

Rubi steps

\begin{align*} \int \left (10 x^9 \cos \left (x^5 \log (x)\right )-x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right )\right ) \, dx &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right ) \, dx\\ &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{14} (1+5 \log (x)) \sin \left (x^5 \log (x)\right ) \, dx\\ &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int \left (x^{14} \sin \left (x^5 \log (x)\right )+5 x^{14} \log (x) \sin \left (x^5 \log (x)\right )\right ) \, dx\\ &=-\left (5 \int x^{14} \log (x) \sin \left (x^5 \log (x)\right ) \, dx\right )+10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{14} \sin \left (x^5 \log (x)\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 0.319045, size = 11, normalized size = 1. \[ x^{10} \cos \left (x^5 \log (x)\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[10*x^9*Cos[x^5*Log[x]] - x^10*(x^4 + 5*x^4*Log[x])*Sin[x^5*Log[x]],x]

[Out]

x^10*Cos[x^5*Log[x]]

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Maple [C]  time = 0.109, size = 30, normalized size = 2.7 \begin{align*}{\frac{{x}^{10}{x}^{i{x}^{5}}}{2}}+{\frac{{x}^{10}}{2\,{x}^{i{x}^{5}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x^9*cos(x^5*ln(x))-x^10*(x^4+5*x^4*ln(x))*sin(x^5*ln(x)),x)

[Out]

1/2*x^10*x^(I*x^5)+1/2*x^10/(x^(I*x^5))

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Maxima [A]  time = 1.20728, size = 15, normalized size = 1.36 \begin{align*} x^{10} \cos \left (x^{5} \log \left (x\right )\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm="maxima")

[Out]

x^10*cos(x^5*log(x))

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Fricas [A]  time = 2.15781, size = 30, normalized size = 2.73 \begin{align*} x^{10} \cos \left (x^{5} \log \left (x\right )\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm="fricas")

[Out]

x^10*cos(x^5*log(x))

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x**9*cos(x**5*ln(x))-x**10*(x**4+5*x**4*ln(x))*sin(x**5*ln(x)),x)

[Out]

Timed out

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Giac [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm="giac")

[Out]

Timed out