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