3.2.60 \(\int \frac {1}{(d+e x) (a+b \text {ArcTan}(c x))} \, dx\) [160]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{(d+e x) (a+b \text {ArcTan}(c x))},x\right ) \]

[Out]

Unintegrable(1/(e*x+d)/(a+b*arctan(c*x)),x)

________________________________________________________________________________________

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 = {} \begin {gather*} \int \frac {1}{(d+e x) (a+b \text {ArcTan}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((d + e*x)*(a + b*ArcTan[c*x])),x]

[Out]

Defer[Int][1/((d + e*x)*(a + b*ArcTan[c*x])), x]

Rubi steps

\begin {align*} \int \frac {1}{(d+e x) \left (a+b \tan ^{-1}(c x)\right )} \, dx &=\int \frac {1}{(d+e x) \left (a+b \tan ^{-1}(c x)\right )} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(d+e x) (a+b \text {ArcTan}(c x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((d + e*x)*(a + b*ArcTan[c*x])),x]

[Out]

Integrate[1/((d + e*x)*(a + b*ArcTan[c*x])), x]

________________________________________________________________________________________

Maple [A]
time = 2.75, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (e x +d \right ) \left (a +b \arctan \left (c x \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x+d)/(a+b*arctan(c*x)),x)

[Out]

int(1/(e*x+d)/(a+b*arctan(c*x)),x)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm="maxima")

[Out]

integrate(1/((b*arctan(c*x) + a)*(x*e + d)), x)

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm="fricas")

[Out]

integral(1/(a*x*e + a*d + (b*x*e + b*d)*arctan(c*x)), x)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a + b \operatorname {atan}{\left (c x \right )}\right ) \left (d + e x\right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(a+b*atan(c*x)),x)

[Out]

Integral(1/((a + b*atan(c*x))*(d + e*x)), x)

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm="giac")

[Out]

sage0*x

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{\left (a+b\,\mathrm {atan}\left (c\,x\right )\right )\,\left (d+e\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((a + b*atan(c*x))*(d + e*x)),x)

[Out]

int(1/((a + b*atan(c*x))*(d + e*x)), x)

________________________________________________________________________________________