3.85 \(\int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx\)

Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\frac{1}{x \sqrt{\cos (a+b x)}},x\right ) \]

[Out]

Unintegrable[1/(x*Sqrt[Cos[a + b*x]]), x]

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Rubi [A]  time = 0.0284183, 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 = {} \[ \int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*Sqrt[Cos[a + b*x]]),x]

[Out]

Defer[Int][1/(x*Sqrt[Cos[a + b*x]]), x]

Rubi steps

\begin{align*} \int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx &=\int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx\\ \end{align*}

Mathematica [A]  time = 0.198933, size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*Sqrt[Cos[a + b*x]]),x]

[Out]

Integrate[1/(x*Sqrt[Cos[a + b*x]]), x]

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Maple [A]  time = 0.132, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}{\frac{1}{\sqrt{\cos \left ( bx+a \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/cos(b*x+a)^(1/2),x)

[Out]

int(1/x/cos(b*x+a)^(1/2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{\cos \left (b x + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)^(1/2),x, algorithm="maxima")

[Out]

integrate(1/(x*sqrt(cos(b*x + a))), 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(1/x/cos(b*x+a)^(1/2),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{\cos{\left (a + b x \right )}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)**(1/2),x)

[Out]

Integral(1/(x*sqrt(cos(a + b*x))), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{\cos \left (b x + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)^(1/2),x, algorithm="giac")

[Out]

integrate(1/(x*sqrt(cos(b*x + a))), x)