Sr Examen
Integral de sqrt(x+2)/(1+(x+2)^(1/3)) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ x + 2 | ------------- dx | 3 _______ | 1 + \/ x + 2 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 2}}{\sqrt[3]{x + 2} + 1}\, dx$$
Integral(sqrt(x + 2)/(1 + (x + 2)^(1/3)), (x, 0, 1))
Respuesta (Indefinida)
[src]
_______
\/ 2 + x
/
/ |
| | ____
| _______ | / 2
| \/ x + 2 | \/ u *u
| ------------- dx = C + 2* | ----------- du
| 3 _______ | ____
| 1 + \/ x + 2 | 3 / 2
| | 1 + \/ u
/ |
/
$$\int \frac{\sqrt{x + 2}}{\sqrt[3]{x + 2} + 1}\, dx = C + 2 \int\limits^{\sqrt{x + 2}} \frac{u \sqrt{u^{2}}}{\sqrt[3]{u^{2}} + 1}\, du$$
Gráfica
Respuesta
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6 ___ 5/6 5/6 6 ___
/6 ___\ ___ ___ /6 ___\ 24*\/ 3 6*3 6*2 30*\/ 2
- 6*atan\\/ 2 / - 2*\/ 2 + 2*\/ 3 + 6*atan\\/ 3 / - -------- - ------ + ------ + --------
7 5 5 7
$$- 6 \operatorname{atan}{\left(\sqrt[6]{2} \right)} - \frac{24 \sqrt[6]{3}}{7} - \frac{6 \cdot 3^{\frac{5}{6}}}{5} - 2 \sqrt{2} + \frac{6 \cdot 2^{\frac{5}{6}}}{5} + 2 \sqrt{3} + \frac{30 \sqrt[6]{2}}{7} + 6 \operatorname{atan}{\left(\sqrt[6]{3} \right)}$$
=
=
6 ___ 5/6 5/6 6 ___
/6 ___\ ___ ___ /6 ___\ 24*\/ 3 6*3 6*2 30*\/ 2
- 6*atan\\/ 2 / - 2*\/ 2 + 2*\/ 3 + 6*atan\\/ 3 / - -------- - ------ + ------ + --------
7 5 5 7
$$- 6 \operatorname{atan}{\left(\sqrt[6]{2} \right)} - \frac{24 \sqrt[6]{3}}{7} - \frac{6 \cdot 3^{\frac{5}{6}}}{5} - 2 \sqrt{2} + \frac{6 \cdot 2^{\frac{5}{6}}}{5} + 2 \sqrt{3} + \frac{30 \sqrt[6]{2}}{7} + 6 \operatorname{atan}{\left(\sqrt[6]{3} \right)}$$
-6*atan(2^(1/6)) - 2*sqrt(2) + 2*sqrt(3) + 6*atan(3^(1/6)) - 24*3^(1/6)/7 - 6*3^(5/6)/5 + 6*2^(5/6)/5 + 30*2^(1/6)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.