3.3.55 \(\int \frac {1}{(f+g x)^3 (A+B \log (\frac {e (a+b x)}{c+d x}))} \, dx\) [255]

Optimal. Leaf size=32 \[ \text {Int}\left (\frac {1}{(f+g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )},x\right ) \]

[Out]

Unintegrable(1/(g*x+f)^3/(A+B*ln(e*(b*x+a)/(d*x+c))),x)

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Rubi [A]
time = 0.02, 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 {1}{(f+g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]

[Out]

Defer[Int][1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]

Rubi steps

\begin {align*} \int \frac {1}{(f+g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )} \, dx &=\int \frac {1}{(f+g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 30.38, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(f+g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])),x]

[Out]

Integrate[1/((f + g*x)^3*(A + B*Log[(e*(a + b*x))/(c + d*x)])), x]

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Maple [A]
time = 1.26, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (g x +f \right )^{3} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(g*x+f)^3/(A+B*ln(e*(b*x+a)/(d*x+c))),x)

[Out]

int(1/(g*x+f)^3/(A+B*ln(e*(b*x+a)/(d*x+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(1/(g*x+f)^3/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="maxima")

[Out]

integrate(1/((g*x + f)^3*(B*log((b*x + a)*e/(d*x + c)) + A)), 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(1/(g*x+f)^3/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="fricas")

[Out]

integral(1/(A*g^3*x^3 + 3*A*f*g^2*x^2 + 3*A*f^2*g*x + A*f^3 + (B*g^3*x^3 + 3*B*f*g^2*x^2 + 3*B*f^2*g*x + B*f^3
)*log((b*x + a)*e/(d*x + c))), x)

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Sympy [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(1/(g*x+f)**3/(A+B*ln(e*(b*x+a)/(d*x+c))),x)

[Out]

Timed out

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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(1/(g*x+f)^3/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm="giac")

[Out]

integrate(1/((g*x + f)^3*(B*log((b*x + a)*e/(d*x + c)) + A)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {1}{{\left (f+g\,x\right )}^3\,\left (A+B\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((f + g*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))),x)

[Out]

int(1/((f + g*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))), x)

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