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

Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\frac{1}{x \cos ^{\frac{3}{2}}(a+b x)},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0275547, 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 = {} \[ \int \frac{1}{x \cos ^{\frac{3}{2}}(a+b x)} \, dx \]

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*}

Mathematica [A]  time = 15.3432, size = 0, normalized size = 0. \[ \int \frac{1}{x \cos ^{\frac{3}{2}}(a+b x)} \, dx \]

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]

________________________________________________________________________________________

Maple [F]  time = 180., size = 0, normalized size = 0. \begin{align*} \text{hanged} \end{align*}

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)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \cos \left (b x + a\right )^{\frac{3}{2}}}\,{d x} \end{align*}

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)

________________________________________________________________________________________

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)^(3/2),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \cos \left (b x + a\right )^{\frac{3}{2}}}\,{d x} \end{align*}

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)