3.1.15 \(\int \frac {\tan ^3(a+b x)}{x^2} \, dx\) [15]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\tan ^3(a+b x)}{x^2},x\right ) \]

[Out]

Unintegrable(tan(b*x+a)^3/x^2,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 = {} \begin {gather*} \int \frac {\tan ^3(a+b x)}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Tan[a + b*x]^3/x^2,x]

[Out]

Defer[Int][Tan[a + b*x]^3/x^2, x]

Rubi steps

\begin {align*} \int \frac {\tan ^3(a+b x)}{x^2} \, dx &=\int \frac {\tan ^3(a+b x)}{x^2} \, dx\\ \end {align*}

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Mathematica [A]
time = 3.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tan ^3(a+b x)}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Tan[a + b*x]^3/x^2,x]

[Out]

Integrate[Tan[a + b*x]^3/x^2, x]

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Maple [A]
time = 0.06, size = 0, normalized size = 0.00 \[\int \frac {\tan ^{3}\left (b x +a \right )}{x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tan(b*x+a)^3/x^2,x)

[Out]

int(tan(b*x+a)^3/x^2,x)

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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(tan(b*x+a)^3/x^2,x, algorithm="maxima")

[Out]

(4*b*x*cos(2*b*x + 2*a)^2 + 4*b*x*sin(2*b*x + 2*a)^2 + 2*b*x*cos(2*b*x + 2*a) + 2*(b*x*cos(2*b*x + 2*a) - sin(
2*b*x + 2*a))*cos(4*b*x + 4*a) - (b^2*x^3*cos(4*b*x + 4*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a)^2 + b^2*x^3*sin(4*b*
x + 4*a)^2 + 4*b^2*x^3*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^3*sin(2*b*x + 2*a)^2 + 4*b^2*x^3*cos(2*b*x
+ 2*a) + b^2*x^3 + 2*(2*b^2*x^3*cos(2*b*x + 2*a) + b^2*x^3)*cos(4*b*x + 4*a))*integrate(2*(b^2*x^2 - 3)*sin(2*
b*x + 2*a)/(b^2*x^4*cos(2*b*x + 2*a)^2 + b^2*x^4*sin(2*b*x + 2*a)^2 + 2*b^2*x^4*cos(2*b*x + 2*a) + b^2*x^4), x
) + 2*(b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))/(b^2*x^3*cos(4*b*x
+ 4*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a)^2 + b^2*x^3*sin(4*b*x + 4*a)^2 + 4*b^2*x^3*sin(4*b*x + 4*a)*sin(2*b*x +
2*a) + 4*b^2*x^3*sin(2*b*x + 2*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a) + b^2*x^3 + 2*(2*b^2*x^3*cos(2*b*x + 2*a) + b
^2*x^3)*cos(4*b*x + 4*a))

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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(tan(b*x+a)^3/x^2,x, algorithm="fricas")

[Out]

integral(tan(b*x + a)^3/x^2, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tan ^{3}{\left (a + b x \right )}}{x^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tan(b*x+a)**3/x**2,x)

[Out]

Integral(tan(a + b*x)**3/x**2, x)

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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(tan(b*x+a)^3/x^2,x, algorithm="giac")

[Out]

integrate(tan(b*x + a)^3/x^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {{\mathrm {tan}\left (a+b\,x\right )}^3}{x^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tan(a + b*x)^3/x^2,x)

[Out]

int(tan(a + b*x)^3/x^2, x)

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