Sr Examen
Integral de root(2x,6)/(1+cbrt(2x)) dx
Solución
Ha introducido
[src]
1 / | | ____ ________ | \/ -2 *\/ x*(-1) | ----------------- dx | 3 _____ | 1 + \/ 2*x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{-2} \sqrt{\left(-1\right) x}}{\sqrt[3]{- \left(-1\right) 2 x} + 1}\, dx$$
Integral((sqrt(-2)*sqrt(x*(-1)))/(1 + (2*x)^(1/3)), (x, 0, 1))
Respuesta (Indefinida)
[src]
___ ___
\/ 2 *\/ x
/
/ |
| | _____
| ____ ________ | / 2
| \/ -2 *\/ x*(-1) | \/ -u *u
| ----------------- dx = C + I* | ----------- du
| 3 _____ | ____
| 1 + \/ 2*x | 3 / 2
| | 1 + \/ u
/ |
/
$$\int \frac{\sqrt{-2} \sqrt{\left(-1\right) x}}{\sqrt[3]{- \left(-1\right) 2 x} + 1}\, dx = C + i \int\limits^{\sqrt{2} \sqrt{x}} \frac{u \sqrt{- u^{2}}}{\sqrt[3]{u^{2}} + 1}\, du$$
Gráfica
Respuesta
[src]
/ 2/3 3 ___ ___ /6 ___\\
___ | 15*2 3*\/ 2 3*\/ 2 *atan\\/ 2 /|
\/ 2 *|1 - ------- - ------- + -------------------|
\ 14 5 2 /
$$\sqrt{2} \left(- \frac{15 \cdot 2^{\frac{2}{3}}}{14} - \frac{3 \sqrt[3]{2}}{5} + 1 + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt[6]{2} \right)}}{2}\right)$$
=
=
/ 2/3 3 ___ ___ /6 ___\\
___ | 15*2 3*\/ 2 3*\/ 2 *atan\\/ 2 /|
\/ 2 *|1 - ------- - ------- + -------------------|
\ 14 5 2 /
$$\sqrt{2} \left(- \frac{15 \cdot 2^{\frac{2}{3}}}{14} - \frac{3 \sqrt[3]{2}}{5} + 1 + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt[6]{2} \right)}}{2}\right)$$
sqrt(2)*(1 - 15*2^(2/3)/14 - 3*2^(1/3)/5 + 3*sqrt(2)*atan(2^(1/6))/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.