3.2.27 \(\int \frac {\sqrt {a+b \log (c x^n)}}{d+e x} \, dx\) [127]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\sqrt {a+b \log \left (c x^n\right )}}{d+e x},x\right ) \]

[Out]

Unintegrable((a+b*ln(c*x^n))^(1/2)/(e*x+d),x)

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Rubi [A]
time = 0.03, 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 {\sqrt {a+b \log \left (c x^n\right )}}{d+e x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sqrt[a + b*Log[c*x^n]]/(d + e*x),x]

[Out]

Defer[Int][Sqrt[a + b*Log[c*x^n]]/(d + e*x), x]

Rubi steps

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

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Mathematica [A]
time = 7.60, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {a+b \log \left (c x^n\right )}}{d+e x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x),x]

[Out]

Integrate[Sqrt[a + b*Log[c*x^n]]/(d + e*x), x]

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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {a +b \ln \left (c \,x^{n}\right )}}{e x +d}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*ln(c*x^n))^(1/2)/(e*x+d),x)

[Out]

int((a+b*ln(c*x^n))^(1/2)/(e*x+d),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*log(c*x^n))^(1/2)/(e*x+d),x, algorithm="maxima")

[Out]

integrate(sqrt(b*log(c*x^n) + a)/(x*e + d), 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((a+b*log(c*x^n))^(1/2)/(e*x+d),x, algorithm="fricas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*ln(c*x**n))**(1/2)/(e*x+d),x)

[Out]

Integral(sqrt(a + b*log(c*x**n))/(d + e*x), 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*log(c*x^n))^(1/2)/(e*x+d),x, algorithm="giac")

[Out]

integrate(sqrt(b*log(c*x^n) + a)/(x*e + d), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\sqrt {a+b\,\ln \left (c\,x^n\right )}}{d+e\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*log(c*x^n))^(1/2)/(d + e*x),x)

[Out]

int((a + b*log(c*x^n))^(1/2)/(d + e*x), x)

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