Sr Examen
Integral de (arctg3x)/x^(5/3) dx
Solución
Ha introducido
[src]
oo / | | atan(3*x) | --------- dx | 5/3 | x | / 0
$$\int\limits_{0}^{\infty} \frac{\operatorname{atan}{\left(3 x \right)}}{x^{\frac{5}{3}}}\, dx$$
Integral(atan(3*x)/x^(5/3), (x, 0, oo))
Respuesta (Indefinida)
[src]
/ | 6 ___ / 3 ___ 2/3 6 ___ 3 ___\ 2/3 /3 ___ 3 ___\ 2/3 / ___ 3 ___ 3 ___\ 2/3 / ___ 3 ___ 3 ___\ 6 ___ / 3 ___ 2/3 6 ___ 3 ___\ | atan(3*x) 9*\/ 3 *log\4*\/ 3 + 12*x - 12*\/ 3 *\/ x / 3*atan(3*x) 3*3 *atan\\/ 3 *\/ x / 3*3 *atan\\/ 3 + 2*\/ 3 *\/ x / 3*3 *atan\- \/ 3 + 2*\/ 3 *\/ x / 9*\/ 3 *log\4*\/ 3 + 12*x + 12*\/ 3 *\/ x / | --------- dx = C - ----------------------------------------------- - ----------- + ------------------------ + ---------------------------------- + ------------------------------------ + ----------------------------------------------- | 5/3 8 2/3 2 4 4 8 | x 2*x | /
$$\int \frac{\operatorname{atan}{\left(3 x \right)}}{x^{\frac{5}{3}}}\, dx = C - \frac{9 \sqrt[6]{3} \log{\left(12 x^{\frac{2}{3}} - 12 \sqrt[6]{3} \sqrt[3]{x} + 4 \sqrt[3]{3} \right)}}{8} + \frac{9 \sqrt[6]{3} \log{\left(12 x^{\frac{2}{3}} + 12 \sqrt[6]{3} \sqrt[3]{x} + 4 \sqrt[3]{3} \right)}}{8} + \frac{3 \cdot 3^{\frac{2}{3}} \operatorname{atan}{\left(\sqrt[3]{3} \sqrt[3]{x} \right)}}{2} + \frac{3 \cdot 3^{\frac{2}{3}} \operatorname{atan}{\left(2 \sqrt[3]{3} \sqrt[3]{x} - \sqrt{3} \right)}}{4} + \frac{3 \cdot 3^{\frac{2}{3}} \operatorname{atan}{\left(2 \sqrt[3]{3} \sqrt[3]{x} + \sqrt{3} \right)}}{4} - \frac{3 \operatorname{atan}{\left(3 x \right)}}{2 x^{\frac{2}{3}}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.