3.1.83 \(\int \frac {x}{\sqrt {\cos (a+b x)}} \, dx\) [83]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {x}{\sqrt {\cos (a+b x)}},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.01, 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 {x}{\sqrt {\cos (a+b x)}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x/Sqrt[Cos[a + b*x]],x]

[Out]

Defer[Int][x/Sqrt[Cos[a + b*x]], x]

Rubi steps

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

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

Verification is not applicable to the result.

[In]

Integrate[x/Sqrt[Cos[a + b*x]],x]

[Out]

Integrate[x/Sqrt[Cos[a + b*x]], x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(x/sqrt(cos(b*x + a)), 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(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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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {\cos {\left (a + b x \right )}}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(x/sqrt(cos(b*x + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {x}{\sqrt {\cos \left (a+b\,x\right )}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/cos(a + b*x)^(1/2),x)

[Out]

int(x/cos(a + b*x)^(1/2), x)

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