Sr Examen
Integral de (dx)/(X^(2)rootx^2-9) dx
Solución
Ha introducido
[src]
6 / | | 1 | ------------- dx | 2 | 2 ___ | x *\/ x - 9 | / 37 -- 10
$$\int\limits_{\frac{37}{10}}^{6} \frac{1}{x^{2} \left(\sqrt{x}\right)^{2} - 9}\, dx$$
Integral(1/(x^2*(sqrt(x))^2 - 9), (x, 37/10, 6))
Respuesta (Indefinida)
[src]
/ ___ 5/6\ / 6 ___ |\/ 3 2*x*3 | / 2 \ | \/ 3 *atan|----- + --------| 2/3 / 2 3 ___ 2/3\ 2/3 | ___ 2/3| | 1 \ 3 9 / 3 *log\x + 3*\/ 3 + x*3 / 3 *log\\/ x - 3 / | ------------- dx = C - ---------------------------- - ------------------------------- + ----------------------- | 2 9 54 27 | 2 ___ | x *\/ x - 9 | /
$$\int \frac{1}{x^{2} \left(\sqrt{x}\right)^{2} - 9}\, dx = C + \frac{3^{\frac{2}{3}} \log{\left(\left(\sqrt{x}\right)^{2} - 3^{\frac{2}{3}} \right)}}{27} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + 3^{\frac{2}{3}} x + 3 \sqrt[3]{3} \right)}}{54} - \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}} x}{9} + \frac{\sqrt{3}}{3} \right)}}{9}$$
Gráfica
Respuesta
[src]
/ ___ 5/6\ / ___ 5/6\ / 2/3\
6 ___ |\/ 3 4*3 | 2/3 /37 2/3\ 6 ___ |\/ 3 37*3 | 2/3 |1369 3 ___ 37*3 |
\/ 3 *atan|----- + ------| 3 *log|-- - 3 | 2/3 / 3 ___ 2/3\ \/ 3 *atan|----- + -------| 2/3 / 2/3\ 3 *log|---- + 3*\/ 3 + -------|
\ 3 3 / \10 / 3 *log\36 + 3*\/ 3 + 6*3 / \ 3 45 / 3 *log\6 - 3 / \100 10 /
- -------------------------- - ------------------- - ------------------------------- + --------------------------- + ------------------ + ----------------------------------
9 27 54 9 27 54
$$- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{4 \cdot 3^{\frac{5}{6}}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + 6 \cdot 3^{\frac{2}{3}} + 36 \right)}}{54} - \frac{3^{\frac{2}{3}} \log{\left(\frac{37}{10} - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(6 - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + \frac{37 \cdot 3^{\frac{2}{3}}}{10} + \frac{1369}{100} \right)}}{54} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{37 \cdot 3^{\frac{5}{6}}}{45} \right)}}{9}$$
=
=
/ ___ 5/6\ / ___ 5/6\ / 2/3\
6 ___ |\/ 3 4*3 | 2/3 /37 2/3\ 6 ___ |\/ 3 37*3 | 2/3 |1369 3 ___ 37*3 |
\/ 3 *atan|----- + ------| 3 *log|-- - 3 | 2/3 / 3 ___ 2/3\ \/ 3 *atan|----- + -------| 2/3 / 2/3\ 3 *log|---- + 3*\/ 3 + -------|
\ 3 3 / \10 / 3 *log\36 + 3*\/ 3 + 6*3 / \ 3 45 / 3 *log\6 - 3 / \100 10 /
- -------------------------- - ------------------- - ------------------------------- + --------------------------- + ------------------ + ----------------------------------
9 27 54 9 27 54
$$- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{4 \cdot 3^{\frac{5}{6}}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + 6 \cdot 3^{\frac{2}{3}} + 36 \right)}}{54} - \frac{3^{\frac{2}{3}} \log{\left(\frac{37}{10} - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(6 - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + \frac{37 \cdot 3^{\frac{2}{3}}}{10} + \frac{1369}{100} \right)}}{54} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{37 \cdot 3^{\frac{5}{6}}}{45} \right)}}{9}$$
-3^(1/6)*atan(sqrt(3)/3 + 4*3^(5/6)/3)/9 - 3^(2/3)*log(37/10 - 3^(2/3))/27 - 3^(2/3)*log(36 + 3*3^(1/3) + 6*3^(2/3))/54 + 3^(1/6)*atan(sqrt(3)/3 + 37*3^(5/6)/45)/9 + 3^(2/3)*log(6 - 3^(2/3))/27 + 3^(2/3)*log(1369/100 + 3*3^(1/3) + 37*3^(2/3)/10)/54
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.