3.84 \(\int \frac{1}{x^4 (a+b \sin (c+d x^3))} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^4 \left (a+b \sin \left (c+d x^3\right )\right )},x\right ) \]

[Out]

Unintegrable[1/(x^4*(a + b*Sin[c + d*x^3])), x]

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Rubi [A]  time = 0.0261377, 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 = {} \[ \int \frac{1}{x^4 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^4*(a + b*Sin[c + d*x^3])),x]

[Out]

Defer[Int][1/(x^4*(a + b*Sin[c + d*x^3])), x]

Rubi steps

\begin{align*} \int \frac{1}{x^4 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx &=\int \frac{1}{x^4 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 0.459977, size = 0, normalized size = 0. \[ \int \frac{1}{x^4 \left (a+b \sin \left (c+d x^3\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^4*(a + b*Sin[c + d*x^3])),x]

[Out]

Integrate[1/(x^4*(a + b*Sin[c + d*x^3])), x]

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Maple [A]  time = 0.041, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{4} \left ( a+b\sin \left ( d{x}^{3}+c \right ) \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^4/(a+b*sin(d*x^3+c)),x)

[Out]

int(1/x^4/(a+b*sin(d*x^3+c)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \sin \left (d x^{3} + c\right ) + a\right )} x^{4}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^4/(a+b*sin(d*x^3+c)),x, algorithm="maxima")

[Out]

integrate(1/((b*sin(d*x^3 + c) + a)*x^4), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{b x^{4} \sin \left (d x^{3} + c\right ) + a x^{4}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^4/(a+b*sin(d*x^3+c)),x, algorithm="fricas")

[Out]

integral(1/(b*x^4*sin(d*x^3 + c) + a*x^4), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{4} \left (a + b \sin{\left (c + d x^{3} \right )}\right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**4/(a+b*sin(d*x**3+c)),x)

[Out]

Integral(1/(x**4*(a + b*sin(c + d*x**3))), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \sin \left (d x^{3} + c\right ) + a\right )} x^{4}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^4/(a+b*sin(d*x^3+c)),x, algorithm="giac")

[Out]

integrate(1/((b*sin(d*x^3 + c) + a)*x^4), x)