3.4 \(\int \frac{a+a \sec (e+f x)}{c+d x} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{a \sec (e+f x)+a}{c+d x},x\right ) \]

[Out]

Unintegrable[(a + a*Sec[e + f*x])/(c + d*x), x]

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Rubi [A]  time = 0.0273671, 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 = {} \[ \int \frac{a+a \sec (e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + a*Sec[e + f*x])/(c + d*x),x]

[Out]

Defer[Int][(a + a*Sec[e + f*x])/(c + d*x), x]

Rubi steps

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

Mathematica [A]  time = 6.48825, size = 0, normalized size = 0. \[ \int \frac{a+a \sec (e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + a*Sec[e + f*x])/(c + d*x),x]

[Out]

Integrate[(a + a*Sec[e + f*x])/(c + d*x), x]

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Maple [A]  time = 0.197, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+a\sec \left ( fx+e \right ) }{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+a*sec(f*x+e))/(d*x+c),x)

[Out]

int((a+a*sec(f*x+e))/(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((a+a*sec(f*x+e))/(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{a \sec \left (f x + e\right ) + a}{d x + c}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((a*sec(f*x + e) + a)/(d*x + c), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} a \left (\int \frac{\sec{\left (e + f x \right )}}{c + d x}\, dx + \int \frac{1}{c + d x}\, dx\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+a*sec(f*x+e))/(d*x+c),x)

[Out]

a*(Integral(sec(e + f*x)/(c + d*x), x) + Integral(1/(c + d*x), x))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((a*sec(f*x + e) + a)/(d*x + c), x)