Sr Examen
Integral de (x^1/2+x^1/3)/(x^1/4-2) dx
Solución
Ha introducido
[src]
1 / | | ___ 3 ___ | \/ x + \/ x | ------------- dx | 4 ___ | \/ x - 2 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt[3]{x} + \sqrt{x}}{\sqrt[4]{x} - 2}\, dx$$
Integral((sqrt(x) + x^(1/3))/(x^(1/4) - 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 2*pi*I\ / 4*pi*I\
-2*pi*I | ------| 2*pi*I | ------|
/ 13 / 2/3 12___\ ------- | 2/3 12___ 3 | ------ | 2/3 12___ 3 |
| -- 3 ___ | 2 *\/ x | 3 ___ 3 | 2 *\/ x *e | 3 ___ 3 | 2 *\/ x *e |
| ___ 3 ___ 5/4 3/4 3 ___ 12___ 5/6 12 7/12 1024*\/ 2 *Gamma(16/3)*log|1 - ----------| 1024*\/ 2 *e *Gamma(16/3)*log|1 - ------------------| 1024*\/ 2 *e *Gamma(16/3)*log|1 - ------------------|
| \/ x + \/ x ___ 4 ___ / 4 ___\ 4*x 16*x 128*\/ x *Gamma(16/3) 1024*\/ x *Gamma(16/3) 64*x *Gamma(16/3) 64*x *Gamma(16/3) 256*x *Gamma(16/3) \ 2 / \ 2 / \ 2 /
| ------------- dx = C + 2*x + 16*\/ x + 64*\/ x + 128*log\-2 + \/ x / + ------ + ------- + --------------------- + ---------------------- + ------------------- + ------------------ + --------------------- + ------------------------------------------ + ----------------------------------------------------------- + ----------------------------------------------------------
| 4 ___ 5 3 Gamma(19/3) Gamma(19/3) 5*Gamma(19/3) 13*Gamma(19/3) 7*Gamma(19/3) 3*Gamma(19/3) 3*Gamma(19/3) 3*Gamma(19/3)
| \/ x - 2
|
/
$$\int \frac{\sqrt[3]{x} + \sqrt{x}}{\sqrt[4]{x} - 2}\, dx = C + \frac{64 x^{\frac{13}{12}} \Gamma\left(\frac{16}{3}\right)}{13 \Gamma\left(\frac{19}{3}\right)} + \frac{256 x^{\frac{7}{12}} \Gamma\left(\frac{16}{3}\right)}{7 \Gamma\left(\frac{19}{3}\right)} + \frac{1024 \sqrt[12]{x} \Gamma\left(\frac{16}{3}\right)}{\Gamma\left(\frac{19}{3}\right)} + \frac{64 x^{\frac{5}{6}} \Gamma\left(\frac{16}{3}\right)}{5 \Gamma\left(\frac{19}{3}\right)} + \frac{4 x^{\frac{5}{4}}}{5} + \frac{16 x^{\frac{3}{4}}}{3} + 64 \sqrt[4]{x} + \frac{128 \sqrt[3]{x} \Gamma\left(\frac{16}{3}\right)}{\Gamma\left(\frac{19}{3}\right)} + 16 \sqrt{x} + 2 x + 128 \log{\left(\sqrt[4]{x} - 2 \right)} + \frac{1024 \sqrt[3]{2} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[12]{x}}{2} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)} + \frac{1024 \sqrt[3]{2} e^{- \frac{2 i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[12]{x} e^{\frac{2 i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)} + \frac{1024 \sqrt[3]{2} e^{\frac{2 i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[12]{x} e^{\frac{4 i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.