3.497 \(\int \frac {\sqrt {g+h x}}{a+b \log (c (d (e+f x)^p)^q)} \, dx\)

Optimal. Leaf size=33 \[ \text {Int}\left (\frac {\sqrt {g+h x}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.08, 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 = {} \[ \int \frac {\sqrt {g+h x}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 1.11, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {g+h x}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {h x + g}}{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}, x\right ) \]

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)),x, algorithm="fricas")

[Out]

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

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

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)),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.36, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {h x +g}}{b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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)),x, algorithm="maxima")

[Out]

integrate(sqrt(h*x + g)/(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 \[ \int \frac {\sqrt {g+h\,x}}{a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )} \,d x \]

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)),x)

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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)),x)

[Out]

Timed out

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