3.3.26 \(\int \frac {1}{1+\tan ^{2 \sqrt {505}}(x)} \, dx\) [226]

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{1+\tan ^{2 \sqrt {505}}(x)},x\right ) \]

[Out]

Unintegrable(1/(tan(x)^(2*505^(1/2))+1),x)

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Rubi [A]
time = 0.01, 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}{1+\tan ^{2 \sqrt {505}}(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 + Tan[x]^(2*Sqrt[505]))^(-1),x]

[Out]

Defer[Int][(1 + Tan[x]^(2*Sqrt[505]))^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {Integral} &=\int \frac {1}{1+\tan ^{2 \sqrt {505}}(x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 3.12, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{1+\tan ^{2 \sqrt {505}}(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(1 + Tan[x]^(2*Sqrt[505]))^(-1),x]

[Out]

Integrate[(1 + Tan[x]^(2*Sqrt[505]))^(-1), x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\tan ^{2 \sqrt {505}}\left (x \right )+1}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(tan(x)^(2*505^(1/2))+1),x)

[Out]

int(1/(tan(x)^(2*505^(1/2))+1),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(1/(tan(x)^(2*505^(1/2))+1),x, algorithm="maxima")

[Out]

-(-1)^(sqrt(101)*sqrt(5))*integrate(((-1)^(sqrt(101)*sqrt(5))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) +
1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1))^2*e^(2*sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*c
os(x) + 1) + 2*sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)) + (-1)^(sqrt(101)*sqrt(5))*e^(2*sqrt
(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 2*sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 - 2*cos(x)
+ 1))*sin(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) + 1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1))
^2 + cos(2*sqrt(101)*sqrt(5)*arctan2(sin(2*x), cos(2*x) + 1))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) +
1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1))*e^(sqrt(101)*sqrt(5)*log(cos(2*x)^2 + sin(2*x)^2 + 2*c
os(2*x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + si
n(x)^2 - 2*cos(x) + 1)) + e^(sqrt(101)*sqrt(5)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + sqrt(101)*sqrt(
5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))*sin(2*
sqrt(101)*sqrt(5)*arctan2(sin(2*x), cos(2*x) + 1))*sin(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) + 1) - 2*sqr
t(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1)))/(2*(-1)^(sqrt(101)*sqrt(5))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(
2*x), cos(2*x) + 1))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) + 1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x),
-cos(x) + 1))*e^(sqrt(101)*sqrt(5)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + sqrt(101)*sqrt(5)*log(cos(
x)^2 + sin(x)^2 + 2*cos(x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)) + (-1)^(2*sqrt(10
1)*sqrt(5))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) + 1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x)
+ 1))^2*e^(2*sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 2*sqrt(101)*sqrt(5)*log(cos(x)^2 + si
n(x)^2 - 2*cos(x) + 1)) + 2*(-1)^(sqrt(101)*sqrt(5))*e^(sqrt(101)*sqrt(5)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(
2*x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x
)^2 - 2*cos(x) + 1))*sin(2*sqrt(101)*sqrt(5)*arctan2(sin(2*x), cos(2*x) + 1))*sin(2*sqrt(101)*sqrt(5)*arctan2(
sin(x), cos(x) + 1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1)) + (-1)^(2*sqrt(101)*sqrt(5))*e^(2*sqrt
(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 2*sqrt(101)*sqrt(5)*log(cos(x)^2 + sin(x)^2 - 2*cos(x)
+ 1))*sin(2*sqrt(101)*sqrt(5)*arctan2(sin(x), cos(x) + 1) - 2*sqrt(101)*sqrt(5)*arctan2(sin(x), -cos(x) + 1))
^2 + (cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(2*sqrt(101)*sqrt(5))*cos(2*sqrt(101)*sqrt(5)*arctan2(sin(2*x)
, cos(2*x) + 1))^2 + (cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(2*sqrt(101)*sqrt(5))*sin(2*sqrt(101)*sqrt(5)*
arctan2(sin(2*x), cos(2*x) + 1))^2), x) + x

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Fricas [A]
time = 0.58, size = 14, normalized size = 0.82 \begin {gather*} {\rm integral}\left (\frac {1}{\tan \left (x\right )^{2 \, \sqrt {505}} + 1}, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(tan(x)^(2*505^(1/2))+1),x, algorithm="fricas")

[Out]

integral(1/(tan(x)^(2*sqrt(505)) + 1), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\tan ^{2 \sqrt {505}}{\left (x \right )} + 1}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(tan(x)**(2*505**(1/2))+1),x)

[Out]

Integral(1/(tan(x)**(2*sqrt(505)) + 1), 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(1/(tan(x)^(2*505^(1/2))+1),x, algorithm="giac")

[Out]

integrate(1/(tan(x)^(2*sqrt(505)) + 1), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {1}{{\mathrm {tan}\left (x\right )}^{2\,\sqrt {505}}+1} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(tan(x)^(2*505^(1/2)) + 1),x)

[Out]

int(1/(tan(x)^(2*505^(1/2)) + 1), x)

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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}

Warning: Unable to verify antiderivative.

[In]

int(1/(tan(x)^(2*505^(1/2))+1),x)

[Out]

not solved

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