3.2.44 \(\int \frac {\sqrt [3]{a+a \sin (c+d x)}}{x} \, dx\) [144]

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

[Out]

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

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Rubi [A]
time = 0.05, 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 {\sqrt [3]{a+a \sin (c+d x)}}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(a + a*Sin[c + d*x])^(1/3)/x,x]

[Out]

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

Rubi steps

\begin {align*} \int \frac {\sqrt [3]{a+a \sin (c+d x)}}{x} \, dx &=\int \frac {\sqrt [3]{a+a \sin (c+d x)}}{x} \, dx\\ \end {align*}

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Mathematica [A]
time = 2.01, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [3]{a+a \sin (c+d x)}}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (a +a \sin \left (d x +c \right )\right )^{\frac {1}{3}}}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (ha
s polynomial part)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + a*sin(c + d*x))^(1/3)/x,x)

[Out]

int((a + a*sin(c + d*x))^(1/3)/x, x)

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