Integrand size = 24, antiderivative size = 24 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\text {Int}\left (\frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x},x\right ) \]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = 3 \text {Subst}\left (\int \frac {\left (a+b \log \left (c (d+e x)^2\right )\right )^p}{x} \, dx,x,\sqrt [3]{x}\right ) \\ \end{align*}
Not integrable
Time = 0.14 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.06 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92
\[\int \frac {{\left (a +b \ln \left (c \left (d +e \,x^{\frac {1}{3}}\right )^{2}\right )\right )}^{p}}{x}d x\]
[In]
[Out]
Not integrable
Time = 0.36 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int { \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )}^{2} c\right ) + a\right )}^{p}}{x} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.33 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int { \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )}^{2} c\right ) + a\right )}^{p}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.06 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int { \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )}^{2} c\right ) + a\right )}^{p}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.76 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )^2\right )\right )^p}{x} \, dx=\int \frac {{\left (a+b\,\ln \left (c\,{\left (d+e\,x^{1/3}\right )}^2\right )\right )}^p}{x} \,d x \]
[In]
[Out]