Integrand size = 17, antiderivative size = 21 \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4 \left (x^3+x^4\right )^{3/4}}{x^2 (1+x)} \]
[Out]
Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2081, 37} \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4 x}{\sqrt [4]{x^4+x^3}} \]
[In]
[Out]
Rule 37
Rule 2081
Rubi steps \begin{align*} \text {integral}& = \frac {\left (x^{3/4} \sqrt [4]{1+x}\right ) \int \frac {1}{x^{3/4} (1+x)^{5/4}} \, dx}{\sqrt [4]{x^3+x^4}} \\ & = \frac {4 x}{\sqrt [4]{x^3+x^4}} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4 x}{\sqrt [4]{x^3 (1+x)}} \]
[In]
[Out]
Time = 0.95 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52
method | result | size |
meijerg | \(\frac {4 x^{\frac {1}{4}}}{\left (1+x \right )^{\frac {1}{4}}}\) | \(11\) |
gosper | \(\frac {4 x}{\left (x^{4}+x^{3}\right )^{\frac {1}{4}}}\) | \(13\) |
risch | \(\frac {4 x}{\left (x^{3} \left (1+x \right )\right )^{\frac {1}{4}}}\) | \(13\) |
pseudoelliptic | \(\frac {4 x}{\left (x^{3} \left (1+x \right )\right )^{\frac {1}{4}}}\) | \(13\) |
trager | \(\frac {4 \left (x^{4}+x^{3}\right )^{\frac {3}{4}}}{x^{2} \left (1+x \right )}\) | \(20\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4 \, {\left (x^{4} + x^{3}\right )}^{\frac {3}{4}}}{x^{3} + x^{2}} \]
[In]
[Out]
\[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\int \frac {1}{\sqrt [4]{x^{3} \left (x + 1\right )} \left (x + 1\right )}\, dx \]
[In]
[Out]
\[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\int { \frac {1}{{\left (x^{4} + x^{3}\right )}^{\frac {1}{4}} {\left (x + 1\right )}} \,d x } \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4}{{\left (\frac {1}{x} + 1\right )}^{\frac {1}{4}}} \]
[In]
[Out]
Time = 5.38 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx=\frac {4\,{\left (x^4+x^3\right )}^{3/4}}{x^2\,\left (x+1\right )} \]
[In]
[Out]