3.1.4 \(\int (a+b \tan (c+d x^2)) \, dx\) [4]

Optimal. Leaf size=17 \[ a x+b \text {Int}\left (\tan \left (c+d x^2\right ),x\right ) \]

[Out]

a*x+b*Unintegrable(tan(d*x^2+c),x)

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Rubi [A]
time = 0.00, 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 \left (a+b \tan \left (c+d x^2\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[a + b*Tan[c + d*x^2],x]

[Out]

a*x + b*Defer[Int][Tan[c + d*x^2], x]

Rubi steps

\begin {align*} \int \left (a+b \tan \left (c+d x^2\right )\right ) \, dx &=a x+b \int \tan \left (c+d x^2\right ) \, dx\\ \end {align*}

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Mathematica [A]
time = 0.80, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+b \tan \left (c+d x^2\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[a + b*Tan[c + d*x^2],x]

[Out]

Integrate[a + b*Tan[c + d*x^2], x]

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Maple [A]
time = 0.11, size = 0, normalized size = 0.00 \[\int a +b \tan \left (d \,x^{2}+c \right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a+b*tan(d*x^2+c),x)

[Out]

int(a+b*tan(d*x^2+c),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(a+b*tan(d*x^2+c),x, algorithm="maxima")

[Out]

a*x + 2*b*integrate(sin(2*d*x^2 + 2*c)/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1
), x)

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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(a+b*tan(d*x^2+c),x, algorithm="fricas")

[Out]

integral(b*tan(d*x^2 + c) + a, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b*tan(d*x**2+c),x)

[Out]

Integral(a + b*tan(c + d*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(a+b*tan(d*x^2+c),x, algorithm="giac")

[Out]

integrate(b*tan(d*x^2 + c) + a, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b*tan(c + d*x^2),x)

[Out]

int(a + b*tan(c + d*x^2), x)

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