Sr Examen
Integral de (2x)/(4+x^3) dx
Solución
Ha introducido
[src]
1 / | | 2*x | ------ dx | 3 | 4 + x | / 0
$$\int\limits_{0}^{1} \frac{2 x}{x^{3} + 4}\, dx$$
Integral((2*x)/(4 + x^3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 3 ___ ___\ / 3 ___ ___ | \/ 3 x*\/ 2 *\/ 3 | | 3 ___ / 2/3\ 3 ___ / 2 3 ___ 2/3\ \/ 2 *\/ 3 *atan|- ----- + -------------| | 2*x \/ 2 *log\x + 2 / \/ 2 *log\x + 2*\/ 2 - x*2 / \ 3 3 / | ------ dx = C - ------------------- + -------------------------------- + ----------------------------------------- | 3 3 6 3 | 4 + x | /
$$\int \frac{2 x}{x^{3} + 4}\, dx = C - \frac{\sqrt[3]{2} \log{\left(x + 2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(x^{2} - 2^{\frac{2}{3}} x + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ___ 3 ___ ___\
3 ___ ___ |\/ 3 \/ 2 *\/ 3 |
3 ___ / 2/3\ 3 ___ / 3 ___\ 3 ___ / 2/3\ 3 ___ / 2/3 3 ___\ \/ 2 *\/ 3 *atan|----- - -----------| 3 ___ ___
\/ 2 *log\1 + 2 / \/ 2 *log\2*\/ 2 / \/ 2 *log\2 / \/ 2 *log\1 - 2 + 2*\/ 2 / \ 3 3 / pi*\/ 2 *\/ 3
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
3 6 3 6 3 18
$$- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{3} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{6} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{18}$$
=
=
/ ___ 3 ___ ___\
3 ___ ___ |\/ 3 \/ 2 *\/ 3 |
3 ___ / 2/3\ 3 ___ / 3 ___\ 3 ___ / 2/3\ 3 ___ / 2/3 3 ___\ \/ 2 *\/ 3 *atan|----- - -----------| 3 ___ ___
\/ 2 *log\1 + 2 / \/ 2 *log\2*\/ 2 / \/ 2 *log\2 / \/ 2 *log\1 - 2 + 2*\/ 2 / \ 3 3 / pi*\/ 2 *\/ 3
- ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + --------------
3 6 3 6 3 18
$$- \frac{\sqrt[3]{2} \log{\left(1 + 2^{\frac{2}{3}} \right)}}{3} - \frac{\sqrt[3]{2} \log{\left(2 \sqrt[3]{2} \right)}}{6} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{\sqrt[3]{2} \log{\left(- 2^{\frac{2}{3}} + 1 + 2 \sqrt[3]{2} \right)}}{6} + \frac{\sqrt[3]{2} \log{\left(2^{\frac{2}{3}} \right)}}{3} + \frac{\sqrt[3]{2} \sqrt{3} \pi}{18}$$
-2^(1/3)*log(1 + 2^(2/3))/3 - 2^(1/3)*log(2*2^(1/3))/6 + 2^(1/3)*log(2^(2/3))/3 + 2^(1/3)*log(1 - 2^(2/3) + 2*2^(1/3))/6 - 2^(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2^(1/3)*sqrt(3)/3)/3 + pi*2^(1/3)*sqrt(3)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.