Optimal. Leaf size=14 \[ -15 x^3+\frac {9}{15625 \log ^4(x)} \]
________________________________________________________________________________________
Rubi [A] time = 0.18, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {12, 6741, 6742, 2302, 30} \begin {gather*} \frac {9}{15625 \log ^4(x)}-15 x^3 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rule 2302
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-36-703125 x^3 \log ^5(x)}{x \log ^5(x)} \, dx}{15625}\\ &=\frac {\int \frac {9 \left (-4-78125 x^3 \log ^5(x)\right )}{x \log ^5(x)} \, dx}{15625}\\ &=\frac {9 \int \frac {-4-78125 x^3 \log ^5(x)}{x \log ^5(x)} \, dx}{15625}\\ &=\frac {9 \int \left (-78125 x^2-\frac {4}{x \log ^5(x)}\right ) \, dx}{15625}\\ &=-15 x^3-\frac {36 \int \frac {1}{x \log ^5(x)} \, dx}{15625}\\ &=-15 x^3-\frac {36 \operatorname {Subst}\left (\int \frac {1}{x^5} \, dx,x,\log (x)\right )}{15625}\\ &=-15 x^3+\frac {9}{15625 \log ^4(x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -15 x^3+\frac {9}{15625 \log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 17, normalized size = 1.21 \begin {gather*} -\frac {3 \, {\left (78125 \, x^{3} \log \relax (x)^{4} - 3\right )}}{15625 \, \log \relax (x)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.24, size = 12, normalized size = 0.86 \begin {gather*} -15 \, x^{3} + \frac {9}{15625 \, \log \relax (x)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 13, normalized size = 0.93
method | result | size |
default | \(-15 x^{3}+\frac {9}{15625 \ln \relax (x )^{4}}\) | \(13\) |
risch | \(-15 x^{3}+\frac {9}{15625 \ln \relax (x )^{4}}\) | \(13\) |
norman | \(\frac {\frac {9}{15625}-15 x^{3} \ln \relax (x )^{4}}{\ln \relax (x )^{4}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 12, normalized size = 0.86 \begin {gather*} -15 \, x^{3} + \frac {9}{15625 \, \log \relax (x)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.11, size = 12, normalized size = 0.86 \begin {gather*} \frac {9}{15625\,{\ln \relax (x)}^4}-15\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 12, normalized size = 0.86 \begin {gather*} - 15 x^{3} + \frac {9}{15625 \log {\relax (x )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________