Sr Examen
Integral de 1/(sqrt(X)*(sqrt^3(x)+36)) dx
Solución
Ha introducido
[src]
9 / | | 1 | ------------------- dx | / 3 \ | ___ | ___ | | \/ x *\\/ x + 36/ | / 4
$$\int\limits_{4}^{9} \frac{1}{\sqrt{x} \left(\left(\sqrt{x}\right)^{3} + 36\right)}\, dx$$
Integral(1/(sqrt(x)*((sqrt(x))^3 + 36)), (x, 4, 9))
Respuesta (Indefinida)
[src]
/ ___ 3 ___ 5/6 ___\ / 2/3 6 ___ | \/ 3 \/ 2 *3 *\/ x | | 2/3 / 3 ___ 2/3 ___\ 2/3 / 2/3 ___\ 2 *\/ 3 *atan|- ----- + ----------------| | 1 6 *log\4*x + 24*\/ 6 - 4*6 *\/ x / 6 *log\6 + \/ x / \ 3 9 / | ------------------- dx = C - --------------------------------------- + ---------------------- + ------------------------------------------- | / 3 \ 108 54 18 | ___ | ___ | | \/ x *\\/ x + 36/ | /
$$\int \frac{1}{\sqrt{x} \left(\left(\sqrt{x}\right)^{3} + 36\right)}\, dx = C + \frac{6^{\frac{2}{3}} \log{\left(\sqrt{x} + 6^{\frac{2}{3}} \right)}}{54} - \frac{6^{\frac{2}{3}} \log{\left(- 4 \cdot 6^{\frac{2}{3}} \sqrt{x} + 4 x + 24 \sqrt[3]{6} \right)}}{108} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}} \sqrt{x}}{9} - \frac{\sqrt{3}}{3} \right)}}{18}$$
Gráfica
Respuesta
[src]
/ ___ 3 ___ 5/6\ / ___ 3 ___ 5/6\
2/3 6 ___ |\/ 3 \/ 2 *3 | 2/3 6 ___ |\/ 3 2*\/ 2 *3 |
2/3 / 2/3\ 2/3 / 2/3 3 ___\ 2/3 / 2/3\ 2/3 / 2/3 3 ___\ 2 *\/ 3 *atan|----- - ----------| 2 *\/ 3 *atan|----- - ------------|
6 *log\2 + 6 / 6 *log\36 - 12*6 + 24*\/ 6 / 6 *log\3 + 6 / 6 *log\16 - 8*6 + 24*\/ 6 / \ 3 3 / \ 3 9 /
- ------------------ - --------------------------------- + ------------------ + -------------------------------- - ----------------------------------- + -------------------------------------
54 108 54 108 18 18
$$- \frac{6^{\frac{2}{3}} \log{\left(- 12 \cdot 6^{\frac{2}{3}} + 36 + 24 \sqrt[3]{6} \right)}}{108} - \frac{6^{\frac{2}{3}} \log{\left(2 + 6^{\frac{2}{3}} \right)}}{54} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{18} - \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{18} + \frac{6^{\frac{2}{3}} \log{\left(- 8 \cdot 6^{\frac{2}{3}} + 16 + 24 \sqrt[3]{6} \right)}}{108} + \frac{6^{\frac{2}{3}} \log{\left(3 + 6^{\frac{2}{3}} \right)}}{54}$$
=
=
/ ___ 3 ___ 5/6\ / ___ 3 ___ 5/6\
2/3 6 ___ |\/ 3 \/ 2 *3 | 2/3 6 ___ |\/ 3 2*\/ 2 *3 |
2/3 / 2/3\ 2/3 / 2/3 3 ___\ 2/3 / 2/3\ 2/3 / 2/3 3 ___\ 2 *\/ 3 *atan|----- - ----------| 2 *\/ 3 *atan|----- - ------------|
6 *log\2 + 6 / 6 *log\36 - 12*6 + 24*\/ 6 / 6 *log\3 + 6 / 6 *log\16 - 8*6 + 24*\/ 6 / \ 3 3 / \ 3 9 /
- ------------------ - --------------------------------- + ------------------ + -------------------------------- - ----------------------------------- + -------------------------------------
54 108 54 108 18 18
$$- \frac{6^{\frac{2}{3}} \log{\left(- 12 \cdot 6^{\frac{2}{3}} + 36 + 24 \sqrt[3]{6} \right)}}{108} - \frac{6^{\frac{2}{3}} \log{\left(2 + 6^{\frac{2}{3}} \right)}}{54} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{18} - \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{18} + \frac{6^{\frac{2}{3}} \log{\left(- 8 \cdot 6^{\frac{2}{3}} + 16 + 24 \sqrt[3]{6} \right)}}{108} + \frac{6^{\frac{2}{3}} \log{\left(3 + 6^{\frac{2}{3}} \right)}}{54}$$
-6^(2/3)*log(2 + 6^(2/3))/54 - 6^(2/3)*log(36 - 12*6^(2/3) + 24*6^(1/3))/108 + 6^(2/3)*log(3 + 6^(2/3))/54 + 6^(2/3)*log(16 - 8*6^(2/3) + 24*6^(1/3))/108 - 2^(2/3)*3^(1/6)*atan(sqrt(3)/3 - 2^(1/3)*3^(5/6)/3)/18 + 2^(2/3)*3^(1/6)*atan(sqrt(3)/3 - 2*2^(1/3)*3^(5/6)/9)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.