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

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (x \sqrt{\cos (a+b x)},x\right ) \]

[Out]

Unintegrable[x*Sqrt[Cos[a + b*x]], x]

________________________________________________________________________________________

Rubi [A]  time = 0.0173204, 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 = {} \[ \int x \sqrt{\cos (a+b x)} \, dx \]

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

Mathematica [F]  time = 0, size = 0, normalized size = 0. \[ \text{\$Aborted} \]

Verification is Not applicable to the result.

[In]

Integrate[x*Sqrt[Cos[a + b*x]],x]

[Out]

$Aborted

________________________________________________________________________________________

Maple [A]  time = 0.464, size = 0, normalized size = 0. \begin{align*} \int x\sqrt{\cos \left ( bx+a \right ) }\, dx \end{align*}

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

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

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

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

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)