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

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

[Out]

Unintegrable(cos(b*x+a)^(1/2)/x,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 = {} \[ \int \frac {\sqrt {\cos (a+b x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[Cos[a + b*x]]/x,x]

[Out]

Defer[Int][Sqrt[Cos[a + b*x]]/x, x]

Rubi steps

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

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Mathematica [A]  time = 0.66, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {\cos (a+b x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[Cos[a + b*x]]/x,x]

[Out]

Integrate[Sqrt[Cos[a + b*x]]/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(cos(b*x+a)^(1/2)/x,x, algorithm="fricas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sqrt(cos(b*x + a))/x, x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {\cos }\left (b x +a \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sqrt(cos(b*x + a))/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(a + b*x)^(1/2)/x,x)

[Out]

int(cos(a + b*x)^(1/2)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sqrt(cos(a + b*x))/x, x)

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