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

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{x \sqrt {\cos (a+b x)}},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {1}{x \sqrt {\cos (a+b x)}} \, dx \]

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*}

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Mathematica [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {\cos (a+b x)}} \, dx \]

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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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

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: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {\cos \left (b x + a\right )}}\,{d x} \]

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)

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maple [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {\cos \left (b x +a \right )}}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {\cos \left (b x + a\right )}}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x\,\sqrt {\cos \left (a+b\,x\right )}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*cos(a + b*x)^(1/2)),x)

[Out]

int(1/(x*cos(a + b*x)^(1/2)), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {\cos {\left (a + b x \right )}}}\, dx \]

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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