3.7.93 \(\int (a+b \sec (c+d x))^{4/3} \, dx\) [693]

Optimal. Leaf size=17 \[ \text {Int}\left ((a+b \sec (c+d x))^{4/3},x\right ) \]

[Out]

Unintegrable((a+b*sec(d*x+c))^(4/3),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 (a+b \sec (c+d x))^{4/3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(a + b*Sec[c + d*x])^(4/3),x]

[Out]

Defer[Int][(a + b*Sec[c + d*x])^(4/3), x]

Rubi steps

\begin {align*} \int (a+b \sec (c+d x))^{4/3} \, dx &=\int (a+b \sec (c+d x))^{4/3} \, dx\\ \end {align*}

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Mathematica [A]
time = 37.65, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b \sec (c+d x))^{4/3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(a + b*Sec[c + d*x])^(4/3),x]

[Out]

Integrate[(a + b*Sec[c + d*x])^(4/3), x]

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Maple [A]
time = 0.07, size = 0, normalized size = 0.00 \[\int \left (a +b \sec \left (d x +c \right )\right )^{\frac {4}{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*sec(d*x+c))^(4/3),x)

[Out]

int((a+b*sec(d*x+c))^(4/3),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*sec(d*x+c))^(4/3),x, algorithm="maxima")

[Out]

integrate((b*sec(d*x + c) + a)^(4/3), x)

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Fricas [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sec(d*x+c))^(4/3),x, algorithm="fricas")

[Out]

Timed out

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b \sec {\left (c + d x \right )}\right )^{\frac {4}{3}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sec(d*x+c))**(4/3),x)

[Out]

Integral((a + b*sec(c + d*x))**(4/3), 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*sec(d*x+c))^(4/3),x, algorithm="giac")

[Out]

integrate((b*sec(d*x + c) + a)^(4/3), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int {\left (a+\frac {b}{\cos \left (c+d\,x\right )}\right )}^{4/3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b/cos(c + d*x))^(4/3),x)

[Out]

int((a + b/cos(c + d*x))^(4/3), x)

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