3.1.94 \(\int \frac {1}{x^2 (a+b \sin (c+d x^3))^2} \, dx\) [94]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x^2 \left (a+b \sin \left (c+d x^3\right )\right )^2},x\right ) \]

[Out]

Unintegrable(1/x^2/(a+b*sin(d*x^3+c))^2,x)

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Rubi [A]
time = 0.02, 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 \frac {1}{x^2 \left (a+b \sin \left (c+d x^3\right )\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x^2*(a + b*Sin[c + d*x^3])^2),x]

[Out]

Defer[Int][1/(x^2*(a + b*Sin[c + d*x^3])^2), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \left (a+b \sin \left (c+d x^3\right )\right )^2} \, dx &=\int \frac {1}{x^2 \left (a+b \sin \left (c+d x^3\right )\right )^2} \, dx\\ \end {align*}

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Mathematica [A]
time = 7.09, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \left (a+b \sin \left (c+d x^3\right )\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/(x^2*(a + b*Sin[c + d*x^3])^2),x]

[Out]

Integrate[1/(x^2*(a + b*Sin[c + d*x^3])^2), x]

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Maple [A]
time = 0.20, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{2} \left (a +b \sin \left (d \,x^{3}+c \right )\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.

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Fricas [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(1/x^2/(a+b*sin(d*x^3+c))^2,x, algorithm="fricas")

[Out]

integral(-1/(b^2*x^2*cos(d*x^3 + c)^2 - 2*a*b*x^2*sin(d*x^3 + c) - (a^2 + b^2)*x^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \left (a + b \sin {\left (c + d x^{3} \right )}\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(x**2*(a + b*sin(c + d*x**3))**2), 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(1/x^2/(a+b*sin(d*x^3+c))^2,x, algorithm="giac")

[Out]

integrate(1/((b*sin(d*x^3 + c) + a)^2*x^2), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x^2\,{\left (a+b\,\sin \left (d\,x^3+c\right )\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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