Integrand size = 21, antiderivative size = 22 \[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\frac {F^a \operatorname {ExpIntegralEi}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
[Out]
Time = 0.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2241} \[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\frac {F^a \operatorname {ExpIntegralEi}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
[In]
[Out]
Rule 2241
Rubi steps \begin{align*} \text {integral}& = \frac {F^a \text {Ei}\left (b (c+d x)^3 \log (F)\right )}{3 d} \\ \end{align*}
Time = 0.18 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\frac {F^a \operatorname {ExpIntegralEi}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
[In]
[Out]
\[\int \frac {F^{a +b \left (d x +c \right )^{3}}}{d x +c}d x\]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 44 vs. \(2 (20) = 40\).
Time = 0.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.00 \[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\frac {F^{a} {\rm Ei}\left ({\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right )}{3 \, d} \]
[In]
[Out]
\[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\int \frac {F^{a + b \left (c + d x\right )^{3}}}{c + d x}\, dx \]
[In]
[Out]
\[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\int { \frac {F^{{\left (d x + c\right )}^{3} b + a}}{d x + c} \,d x } \]
[In]
[Out]
\[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\int { \frac {F^{{\left (d x + c\right )}^{3} b + a}}{d x + c} \,d x } \]
[In]
[Out]
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {F^{a+b (c+d x)^3}}{c+d x} \, dx=\frac {F^a\,\mathrm {ei}\left (b\,\ln \left (F\right )\,{\left (c+d\,x\right )}^3\right )}{3\,d} \]
[In]
[Out]