3.88 \(\int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{x \cos ^{\frac {3}{2}}(a+b x)},x\right ) \]

[Out]

Unintegrable(1/x/cos(b*x+a)^(3/2),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 = {} \[ \int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*Cos[a + b*x]^(3/2)),x]

[Out]

Defer[Int][1/(x*Cos[a + b*x]^(3/2)), x]

Rubi steps

\begin {align*} \int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx &=\int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx\\ \end {align*}

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Mathematica [A]  time = 14.91, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*Cos[a + b*x]^(3/2)),x]

[Out]

Integrate[1/(x*Cos[a + b*x]^(3/2)), 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)^(3/2),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 \[ \int \frac {1}{x \cos \left (b x + a\right )^{\frac {3}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)^(3/2),x, algorithm="giac")

[Out]

integrate(1/(x*cos(b*x + a)^(3/2)), x)

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maple [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \cos \left (b x +a \right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/cos(b*x+a)^(3/2),x)

[Out]

int(1/x/cos(b*x+a)^(3/2),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \cos \left (b x + a\right )^{\frac {3}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)^(3/2),x, algorithm="maxima")

[Out]

integrate(1/(x*cos(b*x + a)^(3/2)), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x\,{\cos \left (a+b\,x\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*cos(a + b*x)^(3/2)),x)

[Out]

int(1/(x*cos(a + b*x)^(3/2)), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \cos ^{\frac {3}{2}}{\left (a + b x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/cos(b*x+a)**(3/2),x)

[Out]

Integral(1/(x*cos(a + b*x)**(3/2)), x)

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