3.251 \(\int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx\)

Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\frac{\tan (a+b x) \sec (a+b x)}{c+d x},x\right ) \]

[Out]

CannotIntegrate[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]

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Rubi [A]  time = 0.0940087, 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 = {} \[ \int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x),x]

[Out]

Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]

Rubi steps

\begin{align*} \int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx &=\int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx\\ \end{align*}

Mathematica [A]  time = 11.2622, size = 0, normalized size = 0. \[ \int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x),x]

[Out]

Integrate[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]

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Maple [A]  time = 0.268, size = 0, normalized size = 0. \begin{align*} \int{\frac{\sec \left ( bx+a \right ) \tan \left ( bx+a \right ) }{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)

[Out]

int(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)

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Maxima [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(sec(b*x+a)*tan(b*x+a)/(d*x+c),x, algorithm="maxima")

[Out]

Timed out

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sec \left (b x + a\right ) \tan \left (b x + a\right )}{d x + c}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x, algorithm="fricas")

[Out]

integral(sec(b*x + a)*tan(b*x + a)/(d*x + c), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)

[Out]

Integral(tan(a + b*x)*sec(a + b*x)/(c + d*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x, algorithm="giac")

[Out]

integrate(sec(b*x + a)*tan(b*x + a)/(d*x + c), x)