3.80 \(\int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx\)

Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\frac{\cos ^{\frac{3}{2}}(a+b x)}{x},x\right ) \]

[Out]

Unintegrable[Cos[a + b*x]^(3/2)/x, x]

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Rubi [A]  time = 0.0279345, 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 = {} \[ \int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Cos[a + b*x]^(3/2)/x,x]

[Out]

Defer[Int][Cos[a + b*x]^(3/2)/x, x]

Rubi steps

\begin{align*} \int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx &=\int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 16.4978, size = 0, normalized size = 0. \[ \int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Cos[a + b*x]^(3/2)/x,x]

[Out]

Integrate[Cos[a + b*x]^(3/2)/x, x]

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Maple [A]  time = 0.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x} \left ( \cos \left ( bx+a \right ) \right ) ^{{\frac{3}{2}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(b*x+a)^(3/2)/x,x)

[Out]

int(cos(b*x+a)^(3/2)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos \left (b x + a\right )^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(b*x+a)^(3/2)/x,x, algorithm="maxima")

[Out]

integrate(cos(b*x + a)^(3/2)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(b*x+a)^(3/2)/x,x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(b*x+a)**(3/2)/x,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos \left (b x + a\right )^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(b*x+a)^(3/2)/x,x, algorithm="giac")

[Out]

integrate(cos(b*x + a)^(3/2)/x, x)