Sr Examen
Integral de 1/((x^(1/2))*x+9) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | ___ | \/ x *x + 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x} x + 9}\, dx$$
Integral(1/(sqrt(x)*x + 9), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 5/6 ___\ / 5/6 | \/ 3 2*3 *\/ x | | 3 ___ / 2/3 ___\ 3 ___ / 3 ___ 2/3 ___\ 2*3 *atan|- ----- + ------------| | 1 2*\/ 3 *log\3 + \/ x / \/ 3 *log\4*x + 12*\/ 3 - 4*3 *\/ x / \ 3 9 / | ----------- dx = C - ------------------------- + ---------------------------------------- + ----------------------------------- | ___ 9 9 9 | \/ x *x + 9 | /
$$\int \frac{1}{\sqrt{x} x + 9}\, dx = C - \frac{2 \sqrt[3]{3} \log{\left(\sqrt{x} + 3^{\frac{2}{3}} \right)}}{9} + \frac{\sqrt[3]{3} \log{\left(- 4 \cdot 3^{\frac{2}{3}} \sqrt{x} + 4 x + 12 \sqrt[3]{3} \right)}}{9} + \frac{2 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}} \sqrt{x}}{9} - \frac{\sqrt{3}}{3} \right)}}{9}$$
Gráfica
Respuesta
[src]
/ 5/6 ___\
5/6 | 2*3 \/ 3 |
3 ___ / 2/3\ 2*3 *atan|- ------ + -----| 3 ___ / 3 ___\ 3 ___ / 2/3 3 ___\ 5/6 3 ___ / 2/3\
2*\/ 3 *log\1 + 3 / \ 9 3 / \/ 3 *log\12*\/ 3 / \/ 3 *log\4 - 4*3 + 12*\/ 3 / pi*3 2*\/ 3 *log\3 /
- --------------------- - ----------------------------- - ------------------- + -------------------------------- + ------- + -----------------
9 9 9 9 27 9
$$- \frac{\sqrt[3]{3} \log{\left(12 \sqrt[3]{3} \right)}}{9} - \frac{2 \sqrt[3]{3} \log{\left(1 + 3^{\frac{2}{3}} \right)}}{9} - \frac{2 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(- \frac{2 \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{9} + \frac{2 \sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{9} + \frac{3^{\frac{5}{6}} \pi}{27} + \frac{\sqrt[3]{3} \log{\left(- 4 \cdot 3^{\frac{2}{3}} + 4 + 12 \sqrt[3]{3} \right)}}{9}$$
=
=
/ 5/6 ___\
5/6 | 2*3 \/ 3 |
3 ___ / 2/3\ 2*3 *atan|- ------ + -----| 3 ___ / 3 ___\ 3 ___ / 2/3 3 ___\ 5/6 3 ___ / 2/3\
2*\/ 3 *log\1 + 3 / \ 9 3 / \/ 3 *log\12*\/ 3 / \/ 3 *log\4 - 4*3 + 12*\/ 3 / pi*3 2*\/ 3 *log\3 /
- --------------------- - ----------------------------- - ------------------- + -------------------------------- + ------- + -----------------
9 9 9 9 27 9
$$- \frac{\sqrt[3]{3} \log{\left(12 \sqrt[3]{3} \right)}}{9} - \frac{2 \sqrt[3]{3} \log{\left(1 + 3^{\frac{2}{3}} \right)}}{9} - \frac{2 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(- \frac{2 \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{9} + \frac{2 \sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{9} + \frac{3^{\frac{5}{6}} \pi}{27} + \frac{\sqrt[3]{3} \log{\left(- 4 \cdot 3^{\frac{2}{3}} + 4 + 12 \sqrt[3]{3} \right)}}{9}$$
-2*3^(1/3)*log(1 + 3^(2/3))/9 - 2*3^(5/6)*atan(-2*3^(5/6)/9 + sqrt(3)/3)/9 - 3^(1/3)*log(12*3^(1/3))/9 + 3^(1/3)*log(4 - 4*3^(2/3) + 12*3^(1/3))/9 + pi*3^(5/6)/27 + 2*3^(1/3)*log(3^(2/3))/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.