Integrand size = 15, antiderivative size = 18 \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4 \left (x^3+x^4\right )^{3/4}}{3 x^3} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2039} \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4 \left (x^4+x^3\right )^{3/4}}{3 x^3} \]
[In]
[Out]
Rule 2039
Rubi steps \begin{align*} \text {integral}& = -\frac {4 \left (x^3+x^4\right )^{3/4}}{3 x^3} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4 (1+x)}{3 \sqrt [4]{x^3 (1+x)}} \]
[In]
[Out]
Time = 0.78 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.61
method | result | size |
meijerg | \(-\frac {4 \left (1+x \right )^{\frac {3}{4}}}{3 x^{\frac {3}{4}}}\) | \(11\) |
gosper | \(-\frac {4 \left (1+x \right )}{3 \left (x^{4}+x^{3}\right )^{\frac {1}{4}}}\) | \(15\) |
trager | \(-\frac {4 \left (x^{4}+x^{3}\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(15\) |
risch | \(-\frac {4 \left (1+x \right )}{3 \left (x^{3} \left (1+x \right )\right )^{\frac {1}{4}}}\) | \(15\) |
pseudoelliptic | \(-\frac {4 \left (x^{3} \left (1+x \right )\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(15\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4 \, {\left (x^{4} + x^{3}\right )}^{\frac {3}{4}}}{3 \, x^{3}} \]
[In]
[Out]
\[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=\int \frac {1}{x \sqrt [4]{x^{3} \left (x + 1\right )}}\, dx \]
[In]
[Out]
\[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=\int { \frac {1}{{\left (x^{4} + x^{3}\right )}^{\frac {1}{4}} x} \,d x } \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4}{3} \, {\left (\frac {1}{x} + 1\right )}^{\frac {3}{4}} \]
[In]
[Out]
Time = 5.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx=-\frac {4\,{\left (x^4+x^3\right )}^{3/4}}{3\,x^3} \]
[In]
[Out]