3.5.100 \(\int \sqrt {g+h x} \sqrt {a+b \log (c (d (e+f x)^p)^q)} \, dx\) [500]

Optimal. Leaf size=35 \[ \text {Int}\left (\sqrt {g+h x} \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )},x\right ) \]

[Out]

Unintegrable((h*x+g)^(1/2)*(a+b*ln(c*(d*(f*x+e)^p)^q))^(1/2),x)

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Rubi [A]
time = 0.20, 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 \sqrt {g+h x} \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]

[Out]

Defer[Int][Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]

Rubi steps

\begin {align*} \int \sqrt {g+h x} \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx &=\int \sqrt {g+h x} \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.75, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {g+h x} \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]],x]

[Out]

Integrate[Sqrt[g + h*x]*Sqrt[a + b*Log[c*(d*(e + f*x)^p)^q]], x]

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Maple [A]
time = 0.19, size = 0, normalized size = 0.00 \[\int \sqrt {h x +g}\, \sqrt {a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((h*x+g)^(1/2)*(a+b*ln(c*(d*(f*x+e)^p)^q))^(1/2),x)

[Out]

int((h*x+g)^(1/2)*(a+b*ln(c*(d*(f*x+e)^p)^q))^(1/2),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((h*x+g)^(1/2)*(a+b*log(c*(d*(f*x+e)^p)^q))^(1/2),x, algorithm="maxima")

[Out]

integrate(sqrt(h*x + g)*sqrt(b*log(((f*x + e)^p*d)^q*c) + a), x)

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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((h*x+g)^(1/2)*(a+b*log(c*(d*(f*x+e)^p)^q))^(1/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((h*x+g)**(1/2)*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 5006 deep

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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((h*x+g)^(1/2)*(a+b*log(c*(d*(f*x+e)^p)^q))^(1/2),x, algorithm="giac")

[Out]

integrate(sqrt(h*x + g)*sqrt(b*log(((f*x + e)^p*d)^q*c) + a), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \sqrt {g+h\,x}\,\sqrt {a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((g + h*x)^(1/2)*(a + b*log(c*(d*(e + f*x)^p)^q))^(1/2),x)

[Out]

int((g + h*x)^(1/2)*(a + b*log(c*(d*(e + f*x)^p)^q))^(1/2), x)

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