3.2.1 \(\int \frac {(e x)^m}{a+b \sin (c+d x^3)} \, dx\) [101]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {(e x)^m}{a+b \sin \left (c+d x^3\right )},x\right ) \]

[Out]

Unintegrable((e*x)^m/(a+b*sin(d*x^3+c)),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 {(e x)^m}{a+b \sin \left (c+d x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(e*x)^m/(a + b*Sin[c + d*x^3]),x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.25, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(e x)^m}{a+b \sin \left (c+d x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (e x \right )^{m}}{a +b \sin \left (d \,x^{3}+c \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

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

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

[Out]

integral((x*e)^m/(b*sin(d*x^3 + c) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (e\,x\right )}^m}{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((e*x)^m/(a + b*sin(c + d*x^3)),x)

[Out]

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

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