3.1.87 \(\int \frac {1}{a+b \sin (c+d x^3)} \, dx\) [87]

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{a+b \sin \left (c+d x^3\right )},x\right ) \]

[Out]

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

________________________________________________________________________________________

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 \frac {1}{a+b \sin \left (c+d x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(a + b*Sin[c + d*x^3])^(-1),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 0.02, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{a+b \sin \left (c+d x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {1}{a +b \sin \left (d \,x^{3}+c \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

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

[Out]

integral(1/(b*sin(d*x^3 + c) + a), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {1}{a+b\,\sin \left (d\,x^3+c\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a + b*sin(c + d*x^3)),x)

[Out]

int(1/(a + b*sin(c + d*x^3)), x)

________________________________________________________________________________________