3.932 \(\int \frac{x^2 \cos (a+b x)}{\sqrt{x^3+3 \sin (a+b x)}} \, dx\)

Optimal. Leaf size=28 \[ \text{CannotIntegrate}\left (\frac{x^2 \cos (a+b x)}{\sqrt{3 \sin (a+b x)+x^3}},x\right ) \]

[Out]

CannotIntegrate[(x^2*Cos[a + b*x])/Sqrt[x^3 + 3*Sin[a + b*x]], x]

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Rubi [A]  time = 0.110789, 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 = {} \[ \int \frac{x^2 \cos (a+b x)}{\sqrt{x^3+3 \sin (a+b x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(x^2*Cos[a + b*x])/Sqrt[x^3 + 3*Sin[a + b*x]],x]

[Out]

Defer[Int][(x^2*Cos[a + b*x])/Sqrt[x^3 + 3*Sin[a + b*x]], x]

Rubi steps

\begin{align*} \int \frac{x^2 \cos (a+b x)}{\sqrt{x^3+3 \sin (a+b x)}} \, dx &=\int \frac{x^2 \cos (a+b x)}{\sqrt{x^3+3 \sin (a+b x)}} \, dx\\ \end{align*}

Mathematica [A]  time = 7.65393, size = 0, normalized size = 0. \[ \int \frac{x^2 \cos (a+b x)}{\sqrt{x^3+3 \sin (a+b x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(x^2*Cos[a + b*x])/Sqrt[x^3 + 3*Sin[a + b*x]],x]

[Out]

Integrate[(x^2*Cos[a + b*x])/Sqrt[x^3 + 3*Sin[a + b*x]], x]

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Maple [A]  time = 0.38, size = 0, normalized size = 0. \begin{align*} \int{{x}^{2}\cos \left ( bx+a \right ){\frac{1}{\sqrt{{x}^{3}+3\,\sin \left ( bx+a \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x)

[Out]

int(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} \cos \left (b x + a\right )}{\sqrt{x^{3} + 3 \, \sin \left (b x + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm="maxima")

[Out]

integrate(x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)), x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} \cos{\left (a + b x \right )}}{\sqrt{x^{3} + 3 \sin{\left (a + b x \right )}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2*cos(b*x+a)/(x**3+3*sin(b*x+a))**(1/2),x)

[Out]

Integral(x**2*cos(a + b*x)/sqrt(x**3 + 3*sin(a + b*x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} \cos \left (b x + a\right )}{\sqrt{x^{3} + 3 \, \sin \left (b x + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm="giac")

[Out]

integrate(x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)), x)