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

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\sec (a+b x)}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\sec (a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sec[a + b*x]/(c + d*x),x]

[Out]

Defer[Int][Sec[a + b*x]/(c + d*x), x]

Rubi steps

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

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Mathematica [A]  time = 4.55, size = 0, normalized size = 0.00 \[ \int \frac {\sec (a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sec[a + b*x]/(c + d*x),x]

[Out]

Integrate[Sec[a + b*x]/(c + d*x), x]

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fricas [A]  time = 0.84, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sec \left (b x + a\right )}{d x + c}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sec(b*x + a)/(d*x + c), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sec \left (b x + a\right )}{d x + c}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sec(b*x + a)/(d*x + c), x)

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maple [A]  time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\sec \left (b x +a \right )}{d x +c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sec \left (b x + a\right )}{d x + c}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sec(b*x + a)/(d*x + c), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cos(a + b*x)*(c + d*x)),x)

[Out]

int(1/(cos(a + b*x)*(c + d*x)), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sec {\left (a + b x \right )}}{c + d x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sec(a + b*x)/(c + d*x), x)

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